How Allah Directs Natural Phenomena

HOW ALLAH DIRECTS NATURAL PHENOMENA

Sakir Kocabas

Summary


In this work we look into how Allah directs what we call “natural phenomena”. Let us remind from the outset that our study is based on the ayahs (= verses) of the Qur’an. For a more detailed study, the sayings of Prophet Muhammad (s.a.w.) on the subject need also be taken into account. Yet, relying on the general principle that there can be no contradiction between the ayahs of the Qur’an and the sayings of the Prophet, we believe that the conclusions that can be derived from the Qur’an about this subject will be sufficient to draw a correct frame to start with.

Before we go on to explore the main subject of this study, we need to recall some of the ayahs in the Qur’an about how Allah, the Creator of the heavens and the earth, has established the order in the heavens and the earth and how He maintains it. For this reason we will first see the ayahs of the Qur’an, which state that Allah is the Real Ruler (= Malik al-Haqq). Secondly, we examine in some detail, the ayahs that express how Allah has established the order in the heavens and how He maintains it. Next, we attempt to bring clarity to the concepts of “physical phenomenon” and “natural phenomenon”. After these definitions we attempt to explore our main subject: How Allah controls and directs physical phenomena and natural phenomena. Finally, we end our survey with a summary of the conclusions.

1. Allah is the Real Ruler (= Malik al-Haqq)

In the Qur’an, there are more than 30 ayahs (= Qur’anic verses) that state that Allah is the Creator of the heavens and the earth.1 Some other ayahs state that Allah’s is the dominion of the heavens and the earth (= lahu mulk as-samawati wa-l ard). Moreover, Allah also states in the Qur’an that He is the Real Ruler (= Malik al-Haqq):

“Exalted is Allah, the Real Ruler; be not in haste with the Qur’an before its revelation to you is completed, but say: My Sustainer, increase me in knowledge.” (Ta-Ha 20/114)

We learn from this ayah an important name of Allah: Malik al-Hakk (= the Real Ruler). We need to dwell on the meaning of this name. Briefly, the above ayah expresses in a clear and succint way that whatever happens in the heavens and the earth happens under the direction and control of Allah. The following ayah on the other hand, states clearly that there is nothing in the heavens and the earth that escapes His knowledge:

“Allah is He who created the seven heavens, and of the earth the like of them [in number]; the instruction (= amr) descends through the midst of them [all]; that you may know that Allah has power over all things and that Allah has encircled all things with knowledge (= wa annallaha qad ahata bi kulli shay’in ‘ilma).” (Talaq 65/12)

“But the god of you all is Allah; there is no god but He; He surrounds all things with knowledge (= wasia kulli shay’in ‘ilma).” (Ta-Ha 20/98)

These ayahs state that Allah has encircled and surrounded everything with knowledge. Moreover, as stated in many other ayahs in the Qur’an, “He is well informed of the actions of His servants (= wallahu khabeerun bi ma ya’malun); “He sees their actions” (= wallahu baseerun bi ma ya’malun); “He hears and sees” (= innahu huwas sami’ul baseer); and as stated in Mulk/67, “He sees everything” (= innahu bi kulli shay’in baseer); in Fatir/38 “Allah knows the secrets of the heavens and the earth (= innallaha ‘alimul ghaybis samawati wal ard); and in the same ayah “indeed He knows the secrets of the hearts (= innahu ‘aleemun bi zatissudur); and in Yunus/10 “… nothing in the heavens and the earth that weighs as an atom (= misqala zarratin), or [anything] smaller or greater than that escapes from His attention (= wa ma ya’zubu ‘an rabbika), all [of this] are in an open book.” It is clearly understood from these ayahs that, all that happens in the heavens and the earth is like an open book to Him, and that nothing happens in the heavens and the earth outside His knowledge.

2. Allah’s is the Administration of the Heavens and the Earth

In the previous section we saw the ayahs which state that Allah is the Real Ruler, and that there is nothing that escapes His knowledge. Yet, His power is not limited to this, for Allah holds in His hand, the Administration (= malakut) of all things:

“Exalted is He in whose hand the is administration of all things (= fa subhan allazi bi yadihi malakutu kulli shay’); you will return to Him.” (Ya-Sin 38/83)

From these verses it is clear that Allah holds the Administration of the heavens and the earth, and He is the Real Ruler. The limited power that He gives to some people in this world for a determined period, is only by His will, and He takes it back when He will.

After we saw the ayahs that state that Allah is the Real Ruler of the heavens and the earth, we are faced with two questions: How does Allah rule the heavens and the earth? Can the human mind comprehend how He rules the heavens and the earth? At first sight these questions may seem to be impossible to answer, yet the answers to both questions can be derived easily from the Qur’an. The next ayah invites mankind to conduct observational and theoretical study on the Administration of the heavens and the earth:

“Have they not studied the administration of the heavens and the earth and what things that Allah has created? (= awa lam yanzuru fi malakut as-samawati wal ardi wa ma khalaqallahu min shay)” (A’raf 7/185)

Another ayah below expresses how Allah actually realizes the Administration, and that this is to be known by mankind:

“Allah is He who has created the seven heavens, and of the earth the like of them; the amr (= instruction) descends through the midst of them so that you may know (= li ya’lamu) that Allah has power over all things and that Allah has encircled everything with knowledge (= wa annallaha qad ahata bi kulli shay’in ‘ilma).” (Talaq 65/12)

In this ayah the word “amr” (= instruction/command) is a particularly important keyword for understanding the administration of the heavens and the earth. As can be understood from the ayah, Allah rules the heavens and the earth by His amr. But what is amr and what is its function in the administration? In order to understand this, we have to look into the ayahs in the Qur’an that this word and its derivatives occur. We attempt to explain briefly what this word refers to in the ayahs next.3

3. The Word Amr in the Qur’an and the Order in the Heavens

In the Qur’an, in relation to the creation and the administration of the heavens, the word amr appears in the ayahs in three principal frames:4

1) The amr that has been revealed into the heavens during their creation, by which the primary order has been established . (We call this the “primary amr”.)

2) The amr that is sent by Allah to influence and control the events in the world. (We call this the “secondary amr”.) With this amr, which He sends down by His angels and which is directly subject to His permission (= izn), Allah can change the current order in any region of space, and can create new and unseen events by it.5

3) The amr that will terminate the current order in the heavens and the earth, which in the Qur’an is called the amr of the Hour (= amr as-Saah).

We can now take a closer look at how the word amr takes place in these three contexts.

The order in the Heavens: The primary amr

The use of the word “amr” together with the words “sakhara” (= make dependent) and “qadr” (= measure) in the ayahs in the first sense above, is closely related with how the order has been established and maintained in the heavens. This is made clear by the ayahs which state that the seven heavens have been revealed in (or loaded with) their instructions with their creation, and that the states of the heavens and of the objects in them are maintained by this amr:

“And in two days He decreed (= qada) them [the heaven and the earth] as the seven heavens, and revealed in each heaven its instruction (= wa awha fi kulli samain amraha) ...” (Fussilat 41/12)

“The sun, the moon and the stars are all subjected [to remain in their courses] by His instruction (= musakharatun bi amrihi).” (A’raf 7/54, Ibrahim 14/33)

“And one of His signs is that the heaven and the earth stands with His amr (= an taqum as-samau wal ardu bi amrihi) ...” (Rum 30/25)

“Did you not see that Allah has made subject to you whatever is on the earth? Ships flow by His amr; He holds the heaven from falling on earth so that it would not fall, except by His permission (= izn); Allah is Most Kind and Most Merciful to mankind.” (Haj 22/65)

As can be seen, the order in the heavens is established and maintained by the (primary) amr that has been revealed in them by Allah. In this case, whatever happens in the heavens must happen in accordance with this amr, so long as there is no other intervention by Allah.6

This understanding leads us to an interesting concept of science, such that in this conceptual framework the aim of scientific investigation becomes understanding and explicating the structure and distribution of the instruction that has been revealed in the heavens by the Creator. An understanding of science as such, would not only explain many things about the order and harmony in the known space, but also would bring clarity to the issue of the creation and formation of the objects in the space. No cosmology developed to date has the basic concepts by which the extremely complicated, and yet excellent order that we observe from the micro-world to the macro-world, can be explained in a consistent way. How did, from a small number of basic physical forces, evolve the wonderously rich physical, chemical, biological and psychological interactions in the world? Is there a cosmic plan behind all this? These are the questions which occupy the minds of many scientists working in the fields of physics and cosmology.7

From the ayahs related with the primary amr in the Qur’an, we can infer that the order in the heavens emerge as a result of the interactions of the instructions (= amr) dispersed in all regions of space (= makan). In this case, the word “amr” (= instruction) emerges as a fundamental concept directly related with “being”. In information physics, the concept of information is used as a basic concept in explaining the degree of order (or the negative entropy) of physical systems.8 But there are categorical differences between the concepts of amr and information: It seems that the primary amr is a set of instructions which not only determines the order in a region of space, but also brings about what we call “matter” itself. From this, we can say that the concept of amr, unlike the concept of information, is a concept related with “being”, or in philosophical terms, is an ontological concept. (Indeed, in a number of ayahs the word amr occurs in close relation with the word kun (= be); see e.g. ayahs in Baqarah 2/117, Al-i Imran 3/47, Maryam 19/35, Mu’min 40/68, Ya-Sin 36/82).

At this point, we are faced with the question whether the primary amr is sufficient in itself or not, in maintaining the order in the heavens as an important question. Before we make a judgement on this issue, we need to consider the ayah:

“It is Allah who holds the heavens and the earth from collapse (= yumsiku-s samawati wal arda an tazula); if they should collapse, there is none, not one can hold them therafter; verily He is most Forbearing, oft Forgiving.” (Fatir 35/4)

This ayah brings several possibilities in mind. The first one is that the verb “holds” (= yumsiku) can be understood as “holds with His amr”, so that when the effects of the primary amr is obliterated by Allah, there would be no one other than Him to bring back the order. The ayah in Rum 30/25 that we saw earlier strengthens this possibility. The second one is that the heavens are protected from reduction or collapse, such that the word “tazula” which is a derivative of “zawal” (= reduction, collapse) may be pointing to such possibility.9

Another possibility is that, the cosmic order which has been established by the primary amr cannot go on indefinitely by itself, and that Allah maintains the order by His secondary amr. It is also imaginable that both possibilities can be the case. Other possibilities than what we said here in a theoretical and speculative framework need also be considered and investigated.

Allah’s intervention to the events in this world: The secondary amr

Let us continue with the relationships between the word amr and the order in the heavens. Since the order in the heavens has been established by the primary amr that has been revealed in them, one might think: If we have a complete understanding of the primary amr which have been revealed in the heavens, and consequently to all systems in them, we can understand all that happens in them. In this way we can possess complete knowledge about these happenings, and see the future. (This could be the final vision of the contemporary understanding of science.) Yet, as explained in some detail below, the problem is not as simple as this. The main reason is that the amr is not something that cannot be changed, and that its effects cannot be overridden once it has been revealed in these systems. An ayah which we saw earlier, explicitly states that other instructions are being (continuously or periodically) sent down by Allah:

“Allah is He who created the seven heavens, and of the earth the like of them [in number]; the instruction (= amr) descends through the midst of them [all]; that you may know that Allah has power over all things and that Allah has encircled all things with knowledge.” (Talaq 65/12)

Indeed, as will be seen when the conceptual frames of the words amr and all other related words (haqq, qadr, qada, izn, sakhara, sultan, ‘aql, and ruh), the amr is not something that consists of the primary amr. We understand from the ayahs in which the words amr, haqq, izn, qadr, and qada occurs, that the effects of the primary amr can be cancelled, overridden, or entirely new conditions can be created by new amr (the secondary amr) sent down by Allah.

The secondary amr sent by the Real Ruler is what is (in terms of the verbs used in the Qur’an in association with it) determined (mubrim), decided on (mustaqir), measured to a measure (qadaran maqdura), differentiated (yufraqu), directed or administered (yudabbir), sent (mursil), sent down (munzil), distributed (muqassimat), decreed (qada), and infused in (yulqi). The angels are sent down with this amr, and they descend through the heavens with it, and after the amr is obeyed (ata), applied/done (maf’ul) and completed (balagha), the amr ascends (ya’ruj) to Allah, and returns (yurji) to Him. The effects of this amr are sometimes made visible (zahara) to mankind. These verses indicate that the completion of the cycle of amr can be regarded both as periodical and continuous.

Some of the other ayahs directly related with the secondary amr are:

“… an amr from Allah’s presence …” (Maida 5/52, Duhan 44/5)

“Or do they determine the amr? We indeed are the determiner (= mubrimun).” (Zukhruf 43/79)

“…all amr have been decided on (= wa kulli amrin mustaqir).” (Qamar 54/3)

“[Allah] directs the amr from the heaven to the earth (= yudabbir al-amri min as-samai ilal ard); then it ascends (= ya’ruj) to Him in [part of ] a day the measure of which is thousand years in your count.” (Sajda 32/5)

“[Allah] sends / sends down the amr (= mursil/munzil).” (Duhan 44/5, Talaq 65/5)

“Allah’s amr is a measure measured (= qadaran maqdura).” (Ahzab 33/38)

“[A nigt] in which all wise [or mighty] amr are differentiated (= fiha yufraqu kulli amrin hakeem).” (Duhan 44/4)

“The angels and the Spirit (= Ruh) descend in that [night] by the leave (= izn) of their Sustainer from [or with] all amr.” (Qadr 97/4)

“When He decrees an amr, He says: ‘Be!’, and it is (= iza qada amran yaqulu lahu kun fa yakun).” (Baqara 2/117, Al-i Imran 3/47, Maryam 19/35, Mu’min 40/68, Ya-Sin 36/82)

“The amr of Allah has come (= ata amrullah) …” (Nahl 16/1)

“… the amr of Allah is done [or applied] (= wa kana amrullahi maf’ula).” (Nisa 4/47)

“… the amr of Allah has become visible (= zahara amrullah) …” (Tawba 9/48)

“Our amr is but a single [act] like the twinkling of an eye.” (Qamar 54/50)

“… Allah has power over His amr (= wallahu ghalibun ‘ala amrihi), but most among mankind know it not.” (Yusuf 12/21)

There are ayahs in the Qur’an indicating that the angels are given the task of applying the secondary amr. Some of these are,

“We [angels] descend only by the leave of your Sustainer (= wa ma natanazzalu illa bi amri rabbika)…” (Maryam 19/64)

“And to Allah bow all that is in the heavens and in the earth whether moving [living] creatures or the angels; for none are arrogant [before their Sustainer].” (Nahl 16/49-50)

“And they [the angels] speak not before He [speaks], and they act by His amr.” (Anbiya 21/27)

Another two ayahs related with the secondary amr, which particularly attract our attention are,

“Nor can a soul die except by Allah’s leave (= izn), the term being fixed as by wiriting…” (Al-i Imran 3/145)

“For each [person] there are [angels] before and behind him; they protect him from the amr of Allah (= yahfazuna min amrillah). Verily, never will Allah change the condition of a nation until they change what is in their soul; but when Allah wishes the punishment of a nation, there can be no turning it back, nor will they find beside Him any to protect.” (Ra’d 13/11)

As can be seen, the first ayah states no person/soul (= nafs) dies except by Allah’s leave (=bi iznillah) which is associated with an amr. This ayah also shows that all the physical conditions determined by the primary amr would not be sufficient to cause the death of a person, however the seem to be deadly. This issue is made clear by the statement in the last ayah, “they protect him form the amr of Allah” so that these protectors [angels], protect that person from the unbearable and deadly effects of the primary amr.10

All these ayahs clearly indicate that the primary amr that has been revealed in the heavens, may not explain every event that happens in the heavens and the earth, despite that the order in the heavens has primarily been established and is maintained by it. Still, we must not overlook the fact that the primary amr has a basic function in maintaining the cosmic order.

We also see from these ayahs that the decree and its application of the amr that overtakes or overcomes the primary amr in a region of space is totally dependent on Allah’s leave (= izn). This is very important, because without Allah’s leave, the primary emr continues its function, and all makan (= spaces) and all the objects in them continue to carry the properties determined by it. The following ayahs clearly state this,

“Did you not see that Allah has made subject to you whatever is on the earth? Ships flow(= tajree) by His amr; He holds the heaven from falling on the earth so that it would not fall, except by His permission (= izn); Allah is Most Kind and Most Merciful to mankind.” (Haj 22/65)

“… the sun, the moon and the stars are in subjection by His amr; verily in this are signs for a nation who use intellect.” (Nahl 16/12)

As can be seen from these ayahs, the properties and motions of the objects in the heavens are formed by the primary amr, and as long as Allah does not send another amr on them by His izn, their properties and motions will continue. The effective use of objects in the heavens and the forces in them by mankind requires studying these properties and the physical forces that determine these properties. We can say that the basic physical forces emerge as the result of the order (= mizan) that has been placed in the heavens.

We can acquire, by all the activity that we call “scientific research”, only the knowledge of the effects of the primary amr and the established order (= mizan). In the future, even if we should have an excellent knowledge of physics and computation, we can only have the knowledge of predicting the effects of the primary amr in a certain region of space.11 As we will explain shortly, when Allah interferes with His amr in any “natural penomenon” it would be impossible to make any reliable prediction about the processes of that phenomenon by physical methods, because it is impossible to know by any scientific method, when and where the secondary amr will take effect.

The ayahs related with this issue clearly shows that, even if we have a complete knowledge of the primary amr that has been revealed in the heavens, we would still not have a complete and absolute knowledge about the world. Even if we used all our scientific research methods, we cannot obtain even the trace of knowledge of the secondary amr that Allah may send by His leave (= izn), to cancel out or partially or completely change the effects of the primary amr in a region of space. This tells us that even when we possess an excellent science and technology, we should put our reliance and trust only in Allah.

***

We see in some of the ayahs of the Qur’an that a close relationship is made between using intellect and understanding cosmological events. Since the order in the heavens and the earth is the work of Allah, the study and research for understanding this great work should be a paramount duty for mankind, because in this way, the true might of Allah can be better understood and better appreciated.

Besides, these ayahs clearly motivate mankind to reason about the creation of the heavens and to understand the amr which lay beneath the cosmological events, and their effective use for the benefit of mankind. These ayahs also ask mankind to take lessons from such events, and guide them to realize that the life of the Hereafter which Allah promises is far superior to the life of this world. Some of the related ayahs are,

“Indeed, in the creation of the heavens and the earth; in the alternation of the day and night; in the ships which flow (= tajree) in the ocean; in the rain which Allah sends down from the sky and revives the earth with it after its death; in the beasts of all kinds that He scatters throughout the earth; in the redirection (= tasreef) of the winds, and the clouds which they trail like their slaves between the earth and the sky, are signs for a nation who use intellect.” (Baqara 2/164)

“In the alternation of the day and night; in the sustenance which Allah sends down from the sky and revives the earth with it after its death; and in the redirection (= tasreef) of the winds, are signs for a nation who use intellect.” (Jasiya 45/5)

“And such are the parables We set for mankind, but none use intellect on them except those who have knowledge (= wa ma ya’qiluha illal ‘alimun).” (Ankabut 29/43)

In the first two verses above, the word “ya’qilun” (= those who use intellect) refers to those who can see the connection between these ayahs and reality. The same term appears in the following verses which state that the life of the Hereafter is superior to the life of this world:

“… But the home [or life] of the Hereafter (= dar al akhira) is better for the righteous; will you not use intellect?” (A’raf 7/169)

“The things you have been given are but the provision and the glitter of the life of this world; better is Allah’s reward and more lasting. Will you not use intellect?” (Qasas 28/60)

On the other hand, the following ayah states that those who do not use intellect are like cattle, or even lower in guidence:

“Do you think that most of them listen or use intellect? They are like cattle, and even more misguided (= bal hum adall).” (Furqan 25/44)

In the ayah below, a surprising stetement appears: “Whatever is in the heavens” have been given to the use and benefit of mankind:

“[Allah] has subjected (= sakhara) to you whatever is in the heavens and the earth, all from Him; verily in this there are signs (= ayat) for a nation who reflect (=qawmin yatafakkarun).”

In this ayah the expression “all from Him” indicates that the use of all the objects and events, or all the physical forces that form and determine their properties and motions are given, without exception, potentially to all men who strive to understand them. In this ayah we also see that the word “sakhara” (= subjected to) is linked with the phrase “a nation who reflect”. This means that the effective use of the objects and the physical forces in the heavens and the earth will be accomplished by collaborative study and the use of intellect by people as nations, rather than as isolated individuals. This would require of course, a public orientation and participation.

The end of the order in the heavens: The amr of the Hour

The amr which is termed in the Qur’an as the amr of the Hour (= amr-us saah), is the instruction which will terminate the order established with the primary amr. As understood from the ayahs related with the Day of Standing (= yawm al qiyama) in the Qur’an, this amr will take effect in a day which will encompass Resurrection and the Day of Reckoning (= yawm al hisab). This subject is dealt with in detail in another study titled “The Day of Standing in the Qur’an and Traditions”, which we hope to have translated into English soon. After these explanations, we can now go on to the definitions of the terms “physical event” and “natural phenomenon” within this conceptual framework.

4. The Definition of “Physical Event”

After this brief inquiry into the ayahs related with the word amr, we can now attempt to provide a definition of “physical event” within this framework: A physical event or physical phenomenon, is an event which happens only within the context of the primary amr which has been revealed in the heavens with their creation. The characteristic feature of such events is that they are repeatable (or repeatedly observable) by humans in the laboratory and observation conditions. We can say that causality in physical events arises as a result of the order or symmetry (= mizan) laid with the primary amr. Causality can be said to be relevant only in the space of large (or macro) scale interactions. Symmetry is also in effect in most interactions in micro space, but here causality leaves its place to uncertainty due to some fundamental properties of light (= photons?) invariably used in the measurements.

The uncertainty in physical events arises in two categorically different forms: uncertainty in the microworld, and uncertainty in the macroworld. We stated that the first arises from the basic properties of light used in observations and measurements. The second type of uncertainty arises from the difficulties of determining the initial conditions of certain complex physical events. This can be called the statistical uncertainty. The physicists believe that many physical phenomena can be modeled by differential equations. In such models, the main problem is to determine the initial conditions, so that starting with these conditions at a time to, the equations would give the status of the event at time t1. In many physical events, the initial conditions are too complicated to know, but in many others, these are known within statistical limits.

5. The Definiton of “Natural Phenomenon”

The term “natural phenomenon” is mostly used for macro scale events observed in the world and in space. Solar and lunar eclipses, various meteorological events, and earthquakes are regarded as phenomena in this framework. In today’s understanding of science all natural phenomena are believed to be a composition of mere physical events. However, unlike accurately predictable events such as the solar and lunar eclipses, the unpredictibility of meteorological events and earthquakes have led the scientists to consider them in a separate class as “chaotic events”.

Based on this classification, causality in natural phenomena needs to be considered in two different frames. Space events such as the solar and lunar eclipses can be explained by the effects of the physical forces, such as gravity, which determine the orbits of the objects in space. But as the explanations of meteorological and tectonic events require taking into account of a number of different effects at the same time, a complete explanation of such an event becomes impossible. The term “butterfly effect” for meteorological phenomena has been coined by some scientists for this purpose. In meteorological and geological phenomena, many effects such as the particular spatial configuration of the planets in their orbits according to the earth and the sun, solar explosions (or “solar spots”), the impact of large meteors on the earth, and other space events can be at work together. All these effects contribute to the uncertainties in the predictions and explanations of such events.

6. Allah’s Intervention in Physical Events

Earlier, we saw from the ayahs in the Qur’an that Allah intervenes in physical events in any region of space and time by His secondary amr as He wishes (= yuridu/arada) to do so. When Allah’s amr comes to a space-time region, it may result in three different effects: 1) The obstruction or cancellation of the effects of the primary amr in the same region, 2) The strengthening the effects of the primary amr, 3) The emergence of an entirely new set of effects in the same region.

In the first case, Allah’s new amr (the secondary amr) interacts with the primary amr that occupies the same place so as to cancel or weaken its effects.

In the second case, Allah’s amr interacts with the primary amr so as to increase its effects, and in this way, it strengthens and/or focuses the current effects.

In the third case, Allah’s new amr brings about entirely new and previously unseen effects either by opening new space for itself, or by interacting with the primary amr in the same space.

7. Allah’s Intervention to Natural Phenomena

A number of ayahs in the Qur’an clearly describes examples of how Allah intervenes in and directs what we call meteorological and geological events. We shall see some of these ayas shortly. But first, let us consider what may happen when Allah intervenes in natural phenomena. In such cases we can think of four different effects: 1) Delaying or initiating the occurrence of the natural event in order to disperse its distructive effects which would otherwise be caused under the effects of the primary amr, 2) Focusing and directing the effects of the natural event, 3) Increasing the strength of the effects of the event, 4) Bringing about natural events with perceived effects of such kind as previously unseen. Let us now see some of the ayahs which exemplify these four different effects:

“Did you not see that Allah makes the clouds move gently, then joins them together and then makes them into a heap? Then you see the rain emerge from their midst; and He sends down from the sky mountain masses (of clouds) in which is hail; He strikes with it whom He will, and He turns it away from whom He will. The vivid flash of His lightning almost blinds the eyes.” (Nur 24/43)

In this ayah the expression “He strikes with it whom He will, and He turns it away from whom He will” exemplifies the effects of the first and the second type that we listed above. Some ayahs which could be taken as examples for the other two cases are,

“[The nation of] Aad, behaved arrogantly in the land with no just reason, and they said: ‘Who is mightier than us?’ Could they not see that Allah, who created them, was mightier than they? Yet they denied Our signs.” (Fussilat 41/15)

“So We sent against them a furious wind through the days of disaster that We might give them a taste of punishment of humiliation in this life; but more humiliating still, will be the punishment of the life to come. And they will not be helped.” (Fussilat 41/16)

“And the [nation of] Aad; they were destroyed by a furious wind, exceedingly violent.” (Haaqqa 69/6)

“[The nation of Samood] rebelled against the amr of their Sustainer; so the stunning noise [of a thunderbolt] seized them even while they were looking on.” (Zariyat 51/44)

The expression “stunning noise” can be regarded as an example of a previously unseen “phenomenon”. (How “natural” could it be regarded is another matter.) In another unusual “phenomenon”, the nation of Lot were destroyed by the collapse of the land swallowing the whole city with all its population, together with a hail of baked stones [lava stones or meteorites?] from above:

“[The angels] said: O, Lot!, we are messengers from your Sustainer; they [your nation] shall not touch you; depart with your kinfolk with the dead of the night, and none of you look back; as for your wife, she shall suffer the fate of the others. In the morning their hour will come. Is not the morning near?” (Houd 11/81)

“And when our amr came, we turned it [the city] upside down, and let loose upon it a shower of baked-stones spread layer on layer.” (Houd 11/82)

These ayahs describe, clearly with no need for more comments, how these nations were destroyed by what we may still call “natural events”.

At this point, regarding our current subject, we are faced with two extremely important questions: If Allah severely punishes sometimes entire nations, what could be the reasons for such punishments? Could it be known or predicted how such punishments will happen? The answers to these questions can be found in the Qur’an in ayahs where the word “sunnatullah” occur. In the Qur’an, the word “sunnatullah” occurs in reference to certain forms of conduct for people and nations. These laws are not changeable, not for even the Messengers of Allah:

“… no change will you find in the laws of Allah (= fa lan tajida li sunnatillahi tabdeela); and no turning off will you find in the laws of Allah.” (Faatir 35/43)

In the Qur’an these laws of conduct are also referred as “the law of the ancients [past nations]” (= sunnatul awwaleen) in some ayahs. The codes of these laws, or in other words the conditions for them to take effect can be found in the ayahs where the words “haqq” and “sunna” take place. We can summarize some of the conditions of these laws as follows:

- To behave arrogantly in the land with no just reason.

- To secretly devise evil plots.

- To kill the messengers of Allah, and those who instruct with equity.

- To make friends with the subjects of Satan (= shayateen) against Allah.

Let us now see the related ayahs. The first is related with the arrogants:

“[The nation of] Aad, behaved arrogantly in the land with no just reason (=fastakbaru fil ardi bi ghayri-l haqq), and they said: ‘Who is mightier than us?’ Could they not see that Allah, who created them, was mightier than they? Yet they denied Our signs.” (Fussilat 41/15)

The Aad paid in this world the due of their evil conduct by being destroyed by a furious storm:

“So We sent against them a furious storm through the days of disaster that We might give them a taste of punishment of humiliation in this life; but more humiliating still, will be the punishment of the life to come. And they will not be helped.” (Fussilat 41/16)

Another great sin which deserves punishment in this world is to secretly devise evil plots (= makr-us sayyia) against people:

“[Their] arrogance in the land and [their] plotting evil (= istakbaran fil ardi wa makr-us sayyia); evil plots will harm only their authors. Are they looking for other than the law of the ancients? “… no change will you find in the laws of Allah (= fa lan tajida li sunnatillahi tabdeela); and no turning off will you find in the laws of Allah.” (Faatir 35/43)

Related with those who devise evil plots, the following ayahs need also be considered:

“Do those who secretly devise evil plots (= allazina makaru-s sayyiat) feel secure that Allah will not cause the earth to swallow them up, or that the wrath will not seize them from directions they little percieve.” (Nahl 16/45)

“Or that He may not seize them in the midst of their going to and fro, when they cannot escape?” (Nahl 16/46)

“Or that He will not give them over to slow destruction? Yet your Sustainer is Compasionate and Merciful.” (Nahl 16/47)

The expression “your Sustainer is Compassionate and Merciful” can be uderstood as that Allah will save those who were wronged by the hands of the plotters of evil. It can also mean that Allah gives long respite to those who devise evil plots, beside openly warning them off by His words about the due results of their deeds, so that they may take heed and give up their evil deeds.

From these ayahs we understand that such plotters of evil are to be sternly punished in this world in four different ways:

1) Allah will bury them in the ground by a terrible disaster.

2) They will be seized by the wrath from a direction they hardly percieve.

3) They will be seized when they go about doing their business.

4) They will be subjected to a slow destruction.

The past nations which murdered Allah’s messengers, or forcefully drove them away from their homes have been destroyed according to these laws (see, e.g. Isra 17/76-77). Those people who unjustly murdered the individuals who instructed equity among them, have also been destroyed in accordance with these laws:

“As to those who deny Allah’s revelations, and slay the Prophets and slay with no just reason those who instruct with equity among mankind; announce them a grevious penalty.” (Al-i Imran 3/21)

“And We have destined for them intimate companions [shayateen]; who make past and future seem fair to them; well was the word justified against them [or: they deserved the fate] which overtook the parties (= umam) of the jinn and men who have gone before them. They shall assuredly be lost.” (Fussilat 41/25)

The expression “well was the word justified against them” (= haqqat ‘alayhim-ul qawl) in the last ayah can be taken to refer to the laws that have been applied to the ancients.

What we have discussed to this point are the laws by which mankind are punished in this world when they exceed the limits. We can now return to our second question above: Could it be known beforehand how the punishment will come into effect?

It is not possible to predict by which “natural event”, and in fact how sunnatullah will take effect. But since the limits of the conditions of these laws are given in the Qur’an, the pending disaster can be estimated by closely observing the behavior of the society, particularly the behavior of those who command and exercise power in it (e.g., its leaders, elites and the wealthy), as to whether the conditions are fulfilled or not.

There are many ayahs in the Qur’an about how Allah has punished the wrongdoing nations in the past some of which seem to be relevant to the conditions of our time:

“Many a cities have insolently opposed the command of their Sustainer and His Messengers, and we called them to a severe account (= hasabnaha hisaban shadeeda); We punished them with exemplary punishment.” (Talaq 65/8)

“When we decide to destroy a settlement, we first send our command to those of them who live in comfort; if they trangress, so that the word is proved true against them; then We destroy them utterly.” (Isra 17/16)

“We did not wrong them, but they wronged their own souls; when the amr of your Systainer comes (= lamma ja’a amru rabbuka), the deities they invoked other than Allah availed them nothing; they only hastened their ruin.” (Houd 11/101)

Lastly, apart from these ayahs, the following ayah is of great interest regarding what may be expected to happen in the future in this world:

“There is no city (= qarya) but shall be destroyed or sternly punished before the Last Day; that is decreed in the Book (= kana zalika fi-l kitabi mastura).” (Isra 17/58)

It would be the duty of all men and women who think, keep contact with reality and take heed, to be prepared as needs to be prepared before the truth of these ayahs become visible.

Conclusion

Many ayahs in the Qur’an declare that Allah is the Creator of the heavens and the earth, and their Real Ruler. He has encompassed and encircled all things with knowledge. Nothing in the heavens and the earth can ever escape His knowledge. Allah intervenses and directs with His secondary amras He wishes, what we call “natural phenomena” which normally happen within the framework of the primary order which He has established in the heavens by His primary amr. He punishes with them whom He decides among mankind, and turns the destruction away from whom He wishes. Allah has made clear by His laws termed as “sunnatullah” in the Qur’an, under what conditions He sends His punishment on people and nations. These laws are also somewhat related with the order (= mizan) which has been established by their creation. If the limits of these laws are well known, it can be sensed when they will take effect, but except as Allah will, it cannot be known exactly when and how they will take effect. We must strive to understand, by using all the means available to us, the happenings in the heavens and the earth and try to understand reality as a whole. When we do this study in a perfect manner and keep equity about ourselves and our position in this world at the same time, we would better appreciate the true might of Allah (= haqqa qadrihi). We will also realize, as has been written in the Qur’an, that the life of the Hereafter is much superior to the life of this world and will give direction to our lives accordingly. Allah knows the best of all things. Was-salaam.


Notes

1 We call what is termed in the Qur’an “the heavens and the earth” as “the universe”. The validity of the term “universe” is being questioned by some physicists such as David Deutsch, who would prefer the term “multiverse” instead. The repeated use of the expression “the heavens and the earth” in the Qur’an can be viewed as to stress the particular importance of the earth in the heavens, with its being the home of millions of different living species including the humans, and its surprisingly suitable conditions for the sustenance of life. This particular place of the planet earth in the universe has been of great interest to many physicists and cosmologists in recent decades. (See, Ref. 7-b)

2 The expression “yanzuru fi” in this verse refers to both observation and systmatic (theoretical) thinking, and muslim scientists in the Classical Era have derived the term “nazariya” (= theory) from the root of this verb “nazara fi”.

3 For more detailed explanations please see,

- Kocabas, S. “Islam’da Bilginin Temelleri”. Iz Yayincilik, Istanbul, 1997.

(An extended English version of this book is being prepared, and we hope to publish it in the future.)

4 The word “amr” occurs in the Qur’an in other frames than the two we have given here. See, Ref. 3 for details.

5 We must emphasize that the word “amr” is not classified in the Qur’an as “primary amr” and “secondary amr”. We have introduced this distinction from the differences of frames of the use of this word. But the appropriateness of this classification can even be seen from the personal pronouns that are used with the word “amr” in the Qur’an. What we call “the primary amr” corresponds to the uses in the ayahs where the word appears almost exclusively in the form “His amr” with the third person singular pronoun, and our term “the secondary amr” corresponds to the uses of the word as “the amr of Allah”, “Our amr”, and simply “the amr”.

6 Whether this amr can be understood as the “operating system” of the heavens, or as a kind of “software” loaded in the heavens, is a subject that deserves to be seriously considered.

7 See;

a - Davies, P. (1992). “The Mind of God”. Touchstone Books. New York.

b - Barrow, J.D. & Tipler, F. (1996). “The Anthropic Cosmological Principle.” Oxford: Oxford University Press.


8 For information physics, see: Stonier, T. (1990). “Information an the Internal Structure of the Universe”. London: Springer-Verlag.

9 The current theoretical framework about elementary particles involves the protection of the basic building blocks of material existence (e.g. protons and electrons) from decay. As an example, consider protons which are accepted to be one of the basic constituents of hydrogen atoms: Unlike free neutrons; protons can stay for a long period (at least 1030 s.) without decaying into lighter particles (mesons and leptons). Had there not been in effect a particular form of baryonic symmetry between elementary particles, there would be no atoms, and no living and inanimate objects as we know them in the world. The word “tazula” may be taken to refer to preventing such kind of collapse.

10 For detailed information on this subject, see Ref. 3.

11 Despite this, we believe that all scientific research in this direction need to be continued by all means, because only those who have knowledge can see the limits of current scientific knowledge, and can better appreciate the true might of Allah. Also, we need to remember the ayah: “... and say: Could those who know be like those who know not? ...” (Zumar 39/9)

Integration of Research Tasks in Modeling Discoveries in Particle Physics

INTEGRATION OF RESEARCH TASKS IN
MODELING DISCOVERIES IN PARTICLE PHYSICS
Sakir Kocabas

Pat Langley
(langley @ cs.stanford.edu)
Robotics Laboratory, Computer Science Dept.,
Stanford University, Stanford, CA 94305 USA

Abstract:
This paper describes a discovery system, BR-4, which integrates several research tasks in modeling the discovery of certain quantum properties and conservation laws by physicists in this century. The program is directed by consistency and completeness constraints, and has the capabilities of theory formation and theory revision in its domain, and of explaining its knowledge state by these constraints . BR-4 is capable of formulating new elementary particles and particle reactions, and proposing observations to test their existence. The program revises its domain theory when it detects formal and theoretical contradictions, and when its domain theory conflicts with observational data.

-----------
* Also affiliated with ITU, Faculty of Space Sciences and Technology, Istanbul, Turkey.

** Also affiliated with the Institute for the Study of Learning and Expertise, 2451 High St., Palo Alto, CA 94301 USA.

1. Introduction
Computational modeling of discovery has been the focus of attention by several research groups in the last ten years, and a number of models with different capabilities have been developed. These capabilities include goal selection, experime nt design, data collection, expectation setting, quantitative reasoning, concept formation, hypothesis formation, theory formation, theory revision, explanation, and paradigm shifts by qualitative models. In current models only a few of these discovery tasks have been integrated in one system. The integration of discovery tasks continues to be a difficult problem in this reearch area of artificial intelligence.

The subject of this paper is an integrated discovery model BR-4, with the capabilities of theory formation, event prediction, data acquisition, explanation, and theory revision. Before we describe the system and its behavior, it is appropri ate to present some background information about its task domain, particle physics.

1.1. The Domain of Particle Physics

Particle physics studies the nature of elementary particles - the building blocks of matter - and interactions among these entities. The basic phenomena in this field take the form of reactions, similar in many ways to those found in chemistry. For instance, two such observed reactions* are

p + p --> p + n + pi
pio --> g + g


where the symbols p, n, pi, pio and g represent the proton, neutron, pion, pion-zero and gamma particles, respectively.

As in chemistry, physics require that reactions among elementary particles obey certain conservation laws. For instance, one of the most basic laws states that any such reaction conserve electric charge of the particles involved. Electric charge is an example of a quantum property, and one of the main tasks in particle physics concerns the assignment of values for quantum properties such that observed reactions conserve those properties. Thus, both of the above reactions conserve electric charge provided we assign the commonly accepted charges 1 to p, 0 to n, 1 to pi, 0 to pio, and 0 to g. Other assignments are also possible for this pair of reactions, but they would not be consistent with other observed particles.

-----------
* Typically, physicists infer the occurence of such reactions from tracks in cloud chambers and similar evidence. We will not attempt to model this inference process here, and instead will simply treat reactions as though they are directly observed.

The concern with conservation also explains why some particle reactions are never observed. For example, the process of beta decay,

n --> p + e + /nu,

in which a neutron decays into a proton p, an electron e, and an antineutrino /n , has been widely detected, in contrast, the decay of protons, as in the reactions

p -> pi + pio
p -> /e + g

has never been seen despite its inherent plausibility. All three reactions satisfy conservation of energy and electric charge, yet only the first occurs in nature. However, one can explain the absence of the other reactions by the existence of another quantum property, the baryon number, that must also be conserved and that these two reaction would violate. Thus, another central task in particle physics involves the explanation of unobserved reactions through the postulation of new qantum numbers.

Other activities include the postulation of new particles, either on theoretical or empirical grounds, and the prediction of reactions that satisfy known conservation laws. Testing such predictions leads into the realm of experimental particle phsics, which we will not address here. But the above pursuits cover a wide range of behaviors that occur in this scientific field.

The above analysis of the discovery tasks suggests that six basic operations play a central role in particle physics. First, one must have a representation to receive and evaluate data about domain objects and events, Second, for a given set of particles, quantum numbers and observed reactions, one must be able to determine a set of quantum values that satisfy conservation for those reactions. Third, one must have a mechanism to explain the currently observed and unobservable reactions in terms of the constraints of the model. Fourth, one must be able to posit new quantum properties that account for the absence of unobserved reactions. Fifth, one requires an operator that posits new particles and determine their role in known reactions. Finally, one must have some mechanism for predicting reactions that have not yet been observed, but which follow from the current theoretical model. We have incorporated these operators into BR-4, where they play a central role in the process of theory formation and revision. (We will refer to them as Read-Data, Determine-Values, Explain-Event, Posit-Property, Posit-Particle, and Predict-Reaction, respectively.)

Operators of this sort must alter some internal representation that contains hypotheses about the particles, properties, and reactions that exist. This representation can take many forms, but following Valdes-Perez et al. (1993), one can view it as two matrices. One matrix lists particles against quantum properties, with each matrix entry specifying the value for a specific particle on a specific prorperty. The other matrix lists particles against reactions, with an entry containing the total number of times the particle occurs in the reaction. In this light, the operator for determining quantum values alters entries in the first matrix, whereas each of the other three operators (Posit-Property, Posit-Particle, and Predict-Reaction) extends one or both matrices along one of their dimensions.

In the next section we describe the knowledge representation and the discovery operators of BR-4 together with its control structure in modeling several different discovery taks ith illustrative examples from particle physics. This will be followed by a discussion on the system's methods and proections for future work. The paper ends with a summary of the conclusions drawn from this research.

2. The System's Knowledge Representation and Behavior
In this section we describe the program's knowledge representation methods and its behavior in modeling certain discoveries in particle physics. The program uses a structured knowledge representation similar to qualitative schemas as in AbE (O'Rorke et al, 1990) and the other recent discovery models.

2.1. Knowledge Representation

BR-4's knowledge organization distinguishes descriptive and prescriptive knowledge. The former type of knowledge is represented as frames, and the latter as a series of operators and functions. The program has six operators which are named as follows: Read-Data, Determine-Values, Explain-Event, Posit-Property, Posit-Particle and Predict-Reaction.
The main data items of BR-4 are elementary particles and their reactions. Both are represented as frames in the system's knowledge base. Particle frames include the name of the particle, the quantum properties and their values. The general form of a particle frame is as follows:

frame: P (frame name)
class : particle
q1 : v1
q2 : v2
.......
qn : vn.

where P is the name of the particle, q1,...,qn the quantum properties, and v1,...,vn the corresponding quantum values, which can be -1, 0, or 1.
Particle reactions are represented in a similar way, this time containing information about the reactions, such as the particles involved, the reaction conditions, the physical status of the reaction, and its validity under the current theory. The general form of a particle reaction frame is as follows:

frame: reaction
class : physical event
actual status : A
logical status : L, logical_status(N,L)
reactants : R
products : P
active properties : Q, active_properties(N,Q)
reactants properties : Rp, reactants_properties(Q,Rp)
products properties : Pp, products_properties(Q,Pp)
conditions : (Rp = Pp) or (Rp =/= Pp).

where A indicates whether the reaction has been physically observed or unobserved, and L indicates whether the reaction is valid or invalid under the current theoretical knowledge of the system. R and P are the lists of the particles involved in the reaction as the reactants and the products respectively. Q indicates the vector of quantum properties that play an active role in the reaction, while Rp and Pp are the quantum value vectors of the reactants and the products. Normally, particle reactions are added to the program's knowledge base (e.g. for the reaction (n --> p + e + /nu) as follows:

frame: r1
class = reaction
actual status = observed
reactants = [n]
products = [p,e,/nu].

Such input reaction frames are then transformed into the form below by the Read-Data operator acting on the parent frame:

frame: r1,
class = reaction
actual status = observed
logical status = valid
reactants = [n]
products = [p,e,/nu]
active properties = [q0, q1]
reactants properties = [1, 0]
products properties = [1, 0]
conditions = {[1,0] = [1,0]}.

The amended slots are added after their values are calculated by the Read-Data operator. In this wa, the system's domain theory is built, onwhich BR-4's other operators act as described below in a control structure summarized in Figure 1.

___________
| Read Data | <-- new data
|___________|
| |
__|____|___ ___________
| |--->| Explain |
| | |_Event_____|
| | _____|_____
| |--->| Determine |<------
| Domain |<---|_Value_____| |
| Theory | _____|_____ |
| |--->| Posit |_______|
| |<---|_Property__| |
| | _____|_____ |
| |--->| Posit |_______|
| |<---|_Particle__|
| | _____|_____
| |--->| Predict |
|___________|<---|_Reactions_|


Figure 1. BR-4's general control structure in the
discovery of quantum properties

2.2. Theory Formation and Revision

The program starts with a simple domain theory about several particles and a small number of observable reactions. BR-4's theory formation activites are driven by its Explain-Event operator which acts on particle reaction frames, looking for reactions which cannot be explained with the system's consistency and completeness contraints. The consistency condition states that any observed particle reaction must be valid by the system's domain theory, where validity is defined as compliance with the quantum conservation laws. An inconsistent reaction in this sense, is unexplainable by the Explain-Event operator.

There are two heuristics for eliminating such contradictions. One is to revise the quantum values of particles in a depth-first search with backtracking through the space of values, until a consistent value set is found. The second heuristic is to introduce a hidden particle to balance the reaction, in either the input or the output, positing that it actually takes part in the reaction but for some reason is not directly observable. The system then computes the property values for this particle, identifying it with an already known particle, or creating an entirely new particle. The first heuristic is applied by the Determine-Values operator and the second one by Posit-Particle.

The completeness condition is defined over unobserved reactions. Any unobserved particle reaction must be violating some quantum conservation law. If the domain theory of BR-4 contains an unobservable reaction that does not seem to violate a quantum conservation law, then this is also an unexplainable event for the Explain-Event operator. This means that the system's domain theory is incomplete regarding the unobserved reaction. In such cases, the system's Posit-Property operator takes control, which posits a new quantum property also to be conserved in observed particle reactions, but not by the unobserved reactions. Determining the values of this property requires search, first for the particles in the missing reaction, and an embedded search for the values of particles in other reactions. This search is carried out by the Determine-Values operator, and as before, if the system arrives at a partial combination of values that rules out an observed reaction or fails to eliminate the unobserved one, it backtracks and considers alternative paths until it finds an acceptable set.

We can extend the notion of incompleteness to include theories that do not explicitly specify all reactions that follow from them, as occurs when BR-4's Posit-Particle postulates a ne particle. In this situation, the system's Predict-Reactions operator systematically generates all possible reactions (decays and collisions) of the ne particle involving one, two or three other known particles. For each such tentative reaction R, the program predicts that R will occur if it conserves all known properties.

3. Illustrative Examples From Particle Physics
In this section we describe the behavior of BR-4 on three examples of discovery fom the history of particle physics, involving the neutrino, baryon and lepton numbers, and electron and muon numbers.

Table 1. The quantum values of particles known prior
to the discovery of the neutrino.
-----------------------------------------------------
Particle mass charge spin

g 0.0 0 1
e 0.51 -1 1/2
p 938.26 1 1/2
n 939.55 0 1/2
/e 0.51 1 1/2

n 0.0 0 1/2
/n 0.0 0 1/2
-----------------------------------------------------

3.1. Discovery of the Neutrino

Until the early 1930's, scientists knew only a few elementary particles, shown in Table 1 along with their mass and their values on the three known quantum properties, energy, charge and spin. The known reactions were also limited to a small number:


p + p --> p + p
e + /e --> g
g --> e + /e


This situation changed after the discovery of the neutron in 1932, when experiments on beta decay revealed the reaction
n --> p + e

in which a neutron decays into a proton and an electron. However, this reaction was problematic in that it violated the conservation of energy and spin, with the total energy and spin counts unbalanced in the reaction. Rather than abandon the conservation law, physicists postulated the presence of a new particle,* also generated during beta decay, that would balance out the missing energy and spin. Although not visible in the reaction, they inferred the property values for this particle from the values for the other particles in the decay process. They concluded that this neutrino has zero rest mass, no electrical charge, and a spin of one half.

Given the reactions above and the quantum numbers in Table 1, BR-4 responds in a similar manner. The system's Explain-Event operator cannot explain the fourth reaction, as it detect passes control to Posit-Property. This operator considers to assign alternative spin values in an attempt to find a consistent set of values that would balance the reaction. But in this case, BR-4 is not allowed to modify the spin values, as these are assumed to be correctly established by observation. This leaves revision of the unbalanced reaction as the

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* In the early 1930's there were serious debates among physicists as to the validity of the conservation laws in the subatomic world.

Table 2. Particle reactions that were (a) observed and (b) not observed
in experiments after the introduction of the particles in Table 1.
-----------------------------------------------------------------------
a) Observed reactions b) Unobserved reactions

p + p --> p + p p --> /e + g
n --> p + e + /nu p --> /e + e + /e
/e + e --> g p --> /e + g + g
g + p --> e + /e + p
/nu + p --> n + /e
nu + n --> p + e
-----------------------------------------------------------------------

only solution as the control passes to the Posit-Particle operator, which adds an extra particle to the output side of the reaction, giving

n --> p + e + nu.

Using the conservation laws, Determine-Values computes the charge and spin of the new particle, nu, as 0 and 1/2 respectively. Another possible revision would have added a new particle with opposite properties to /n, to the input side of the reaction, but physicists favored the former solution as they were thinking in terms of a decay process.

However, the inclusion of the neutrino and its antiparticle leaves the theory incomplete, in that they imply reactions with other known particles. BR-4's Predict-Reactions operator finds no decays for the neutrino, but it does find three collision reactions that are consistent with the theory:

/nu + p --> n + /e
nu + n --> p + e
nu + /nu --> g

which are predicted to be observed in experiments. The first two of these were later detected by physicists. The third reaction has a very low probablity and is rather difficult to detect.

3.2. Proposing Baryon and Lepton Numbers

The discovery of the neutrino left physicists with seven elementary particles,* having the properties and values shown in Table 1. Physicists realized that the existence of these particles, combined with known quantum conservation laws, implied a variety of reactions. Subsequent observations revealed evidence for the predicted reactions in Table 2 (a) but not for those shown in Table 2 (b). For some reason, the three predicted decays of the proton did not occur in nature. To explain this, physicists proposed a new quantum property, known as the baryon number.**
--------------------
* The neutrino-antineutrino distinction as experimentally verified in the late 1950's.
** Stuckelberg proposed this new quantum property in 1938 as the protonic charge which was later to be called the baryon number.

Table 3. The quantum values for elementary particles known in 1953
after the discovery of baryon and lepton numbers.
--------------------------------------------------------------------
Particle mass charge spin baryon lepton

g 0.00 0 1 0 0
e 0.51 -1 1/2 0 1
p 938.26 1 1/2 1 0
n 939.55 0 1/2 1 0
/e 0.51 1 1/2 0 -1
nu 0.00 0 1/2 0 1
/nu 0.00 0 1/2 0 -1
mu 105.60 -1 1/2 0 1
/mu 105.60 1 1/2 0 -1
pi 139.60 1 - 0 0
/pi 139.60 -1 - 0 0
pio 135.00 0 - 0 0
---------------------------------------------------------------------

BR-4's Predict-Reactions operator proposes the same reactions, but the Explain-Event operator cannot explain the absence of the reactions in Table 2 (b). The program selects the first reaction, p --> /e + g, and turns it into a set of inequalities, each based on a different combination of values for the particles involved. In this case, it would generate the four ineualities

1 =/= 0 + 0
1 =/= 1 + 1
0 =/= 1 + 0
0 =/= 0 + 1

The Determine-Values operator then selects one of these value sets, say the first, p =1, /e = 0, g = 0, and tests them in the observed reactions, say n --> p + e + /nu, this time treating it as an equality, and obtains

n = 1 + 0 + /nu

which leaves the property values for n and /nu unspecified. Two value sets are possible for this pair, n = 1, /nu = 0 and n = 0, /nu = -1. The first value set is consistent with all the then known reactions, while the second set is inconsistent with the reaction nu + n --> p + e. At any point, detection of an unbalanced reaction that violates conservation of the new property causing backtracking to one of the alternative value sets. If the search exhausts all such sets produced from observed reactions, the system backtracks further and considers alternative value sets generated from the unobserved reactions.

Given the experimental results in Table 2, BR-4 arrives at the value zero for all particles except the proton and neutron, to which it assigns the value one. These settings correspond to those obtained by physicists for the baryon number, which successfully explain the absence of the reactions in Table 2 (b).

Alternatively, by using the value set in the third inequality above, BR-4 would propose another quantum property by assigning the following values to particles: p = 0, n = 0, /e = -1, g = 0, and e = 1. These values correspond to the lepton numbers of elementar particles (see, Table 3).

Table 4. Some particle reactions that were (a) observed and (b) not
observed in experiments after the discovery of baryon and lepton numbers.
----------------------------------------------------------------------
a) Observed reactions b) Unobserved reactions

pi --> /nu + mu mu --> e + g
/pi --> mu + /nu pi --> /mu + g
mu --> e + nu + /nu pi --> /e + g
/mu --> /e + /nu + nu
pio --> g + /e + e
pio --> g + g
pio --> e + e + /e + /e
----------------------------------------------------------------------

In 1935, Yukawa had proposed the existence of additional particles with the mass of about 100 MeV in the nucleus. The reasoning behind Yukawa's proposal, which we have not attempted to model, involved energy calculations on atomic nuclei. Later, in the 1940s, observations on cosmic rays revealed five such particles: the muon (mu) and anti-muon (/mu), the pion (pi) and anti-pion (/pi), and the pion-zero (pio), along with the property values in Table 4. Baryon and lepton numbers could explain the possibility and absence of the reactions of these particles in the 1950s. Some of these reactions are given in Table 5(a) and 5 (b).

3.3. Electron and Muon Numbers

With the discovery of the baryon and lepton numbers, physicists had produced a theory, involving 12 elementary particles and four quantum properties plus the relativistic masses of the particles, that was apparently consistent and complete. Table 3 reflects this state of physical knowledge. Some skepticisms remained, such as for the neutrino, which seemed very difficult to observe for theoretical reasons. However, in 1953, experiments revealed indirect evidence for the reaction

/nu + p --> n + /e.

Unfortunately, this reaction occurred when the anti-neutrino n had been generated through beta decay (n p + e + n ), but not when produced through muon decay (m --> e + nu + /nu).

To resolve this dilemma, scientists postulated that the two reactions actually generated two distinct types of neutrinos, calling the former an electron neutrino (ne) and the latter a muon neutrino (nu_mu). This distinction (and the analogous one for anti-neutrinos) introduced two additional rows in the table of particles. However, it also produced the unobserved reactions shown in Table 5(b), which physicists again sought to explain by introducing yet another property, which they named the electron number.

Our model cannot directly explain the historical distinction into two classes of neutrinos, but we believe it constitutes a variation on the heuristic for postulating new particles that originally led to inference of the neutrino. Once this distinction has been made, BR-4 realizes that its current theory is incomplete, in that it cannot explain the unobserved reactions involving the muon neutrino and its antiparticle. Postulating a new property, it searches the space of values using the same process as it used for the baryon and lepton numbers. The resulting values agree with those proposed by physicists for the electron number, but are not sufficient to rule out the unobserved reaction (pi --> /mu + g). Explanation of this omission requires introduction of yet another quantum property, this one corresponding to the muon number, which physicists postulated in 1962.

Table 5. Some particle reactions that were (a) observed and (b) not
observed in experiments after introducing distinction between electron
neutrinos (nu_e) and muon neutrinos (nu_mu).
----------------------------------------------------------------------
a) Observed reactions b) Unobserved reactions

pi --> /mu _ nu_mu mu --> e + g
/pi --> mu + /nu_mu /nu_mu + p --> n + /e
mu --> e + /nu_e + nu_mu nu_mu + n --> p + e

/mu --> /e + nu_e + /nu_mu pi --> /mu + g
pio --> g + e + /e pi --> /e + g
pio --> g + g
pio --> e + /e + e + /e
----------------------------------------------------------------------

4. Discussion of the Framework
Now that we have seen some examples of BR-4's operation, we can consider the implications of the model for research on scientific creativity, related work on scientific discovery, and some directions for future research on this topic.

4.1 Implications of the Model

Modern scientific research is one of the most complex human activities, requiring the use of different types of general and specific knowledge. It can also involve more than a dozen different search spaces ranging from scientific problem formulation through data collection and evaluation, to hypothesis formation, theory formation and theory revision (see, Kocabas, 1993). Within the research activities, different types of discovery and creativity can be distinguished as logico-mathematical, formal, theoretical and empirical discovery. Current computational models have shortcomings in capturing the details of historical discoveries for reasons described by Tweney (1990). However, this should not diminish their usefulness, as they can provide an overall look into the structure of the developments of theories both in their formation and revision processes. They can also be useful in analyzing the historical progress of scientific ideas and of the possibility of alternative ideas together with their implications.

In this study, our aim has not been to model the historical details of particle physics, but to show that certain computational mechanisms can account for theory formation and revision in this domain. The basic mechanisms in BR-4 -- search guided by heuristic knowledge -- bears close resemblance to those implicated in normal human problem solving, as studied by Newell and Simon (1972), as well as many others.

If correct, this view suggests that some of the creative activities in particle physics has much in common with everyday reasoning. However, modern scientific reasoning is much more reliant on logico-mathematical, theoretical and methodological knowledge than everyday reasoning in addition to empirical and commonsense knowledge. Unlike simple search spaces dealt with in everyday reasoning, it also has to deal with a number of different search spaces at the same time if it has to result in discoveries, or even to make progress at all (see, e.g., Klahr, 1994; Kocabas, 1993). Our model operates only in the spaces of empirical hypothesis and theory formation, event prediction, problem formulation and theory revision.

Previous models of scientific discovery, such as those described by Langley, Simon, Bradshaw, and Zytkow (1987), have taken a similar stance on the creative process. However, most such work has focused on limited aspects of scientific reasoning, such as the discovery of laws or the formation of structural theories.

With BR-4, we have attempted to cover a broader range of the discovery process within a unified framework. We described how the system formulates new problems whenever new data reveals its current theory to be either inconsistent or incomplete. In handling problems of inconsistency, BR-4 relies on depth-first search guided by algebraic and domain heuristics to explore the space of values for quantum properties, resorting to the postulation of new particles only if its search fails.

In dealing with incompleteness, the model predicts new reactions that follow from the introduction of new particles and posits new quantum properties to explain why some of these reactions never occur. The introduction of new particles and new properties constitute important examples of theory formation.

Our system does not provide a detailed account of the historical record, but it does explain several impressive discoveries at a more abstract level, using simple mechanisms of a familiar kind. This limited success provides further evidence that at least some types of scientific creativity does not require any special processes, but can be explained as a straightforward extension of existing theories of human cognition.

4.2 Related Work on Scientific Discovery

Our computational model of discovery draws many of its ideas from earlier work in this area. BR-4 is a direct descendant of Zytkow and Simon's (1986) STAHL, which modeled a variety of qualitative discoveries in the history of chemistry. The detection of inconsistencies in reactions played a central role in this system, with one of its responses being the introduction of new elements like phlogiston, which served much the same role in early chemistry as the neutrino did in particle physics.
Rose and Langley (1986) described STAHLp, a rational reconstruction of the earlier system that showed all of its discoveries could be explained in terms of inconsistencies and their resolution. In addition, they used the system to model a number of other reaction-oriented discoveries from the history of science. Moreover, their approach showed that dependency-directed reasoning simplified the theory revision process, letting their STAHLp handle problems with a search-control scheme that relied on simple hill climbing.

The BR-3 system, presented by Kocabas (1991), extended this framework to include the detection of incomplete theories, and the postulation of new properties to explain the absence of reactions. Kocabas applied this idea to the history of particle physics, using it to explain both the origin of several quantum numbers and the particular values assigned to them by scientists. In related work (Kocabas, 1994), he described another system TREV which formulates new particles and new reactions, but this system does not integrate these functions in its discovery process. BR-3 was the immediate precursor of BR-4, differing mainly in that the former lacked the ability to postulate new particles and to predict new reactions.

Valdes-Perez (in press) has described an alternative approach to discovery in particle physics, which he has implemented in the PAULI system. This scheme use a variation on linear programming to search the space of property values, subject to constraints that reflect observed and unobserved reactions. Also, Fischer and Zytkow (1992) have reported on GELL-MANN, a system designed to explain the formation of the quark theory, which also carries out a search through a space of parameter values subject to constraints.

A more general framework, proposed by Valdes-Perez, Simon, and Zytkow (1993), views the process of formulating structural models in terms of matrix operations. They show how many existing systems, including those described above, can be viewed in this light, with the basic operations involving the extension of a matrix along one or more dimensions and the revision of entries in the cells of the matrix. Our own BR-4 system also fits well into this framework, as suggested by our use of Valdes-Perez et al.'s terminology in Section 2.

Other research on theory revision seems less closely related. Rajamoney's (1990) COAST system designs experiments to distinguish between alternative structural models in physics, and Karp's (1990) HypGene uses a similar idea for biological theories. Kulkarni and Simon (1990) describe KEKADA, a computational model that integrates theory revision, experiment design, and problem formulation to model Krebs' discovery of the urea cycle. Shrager and Langley (1990) consider the relations among these systems in more detail.

4.3. Directions for Future Work

Although BR-4 provides an abstract account for some important developments in the history of particle physics, there remains considerable room for extensions to the model. One direction for improvement involves the notion of explanation. In some sense, the current system formulates explanations when it finds that a newly observed reaction is consistent with the existing theory or when it proposes a new property that rules out an unobserved reaction. However, BR-4 does not generate an explicit proof or other structure that connects assumptions and observations. In future work, we plan to model the explanatory process in more detail, with the system deducing the presence or absence of specific reactions from declara tive statements of quantum properties and conservation laws. In turn, this may let us recast BR-4's operators in terms of an abduction process (Ng & Mooney, 1990; O'Rorke et al., 1990) that modifies assumptions to explain known phenomena.

We also hope to extend the system to handle the introduction of componential models, which describe particles at one level as combinations of more primitive particles. Langley et al.'s (1987) DALTON took some initial steps along these lines to explain the relations between chemical molecules and elements, but we believe that we can adapt BR-4 to explain the origins of the quark theory and its alternatives. The basic task here involves explaining why elementary particles with some quantum properties exist and others do not. The constraints of consistency and completeness, which play such a central role in BR-4, seem well suited for this problem, which involves postulating new component particles (quarks), then searching the space of quantum values and their compositions that satisfy certain constraints (e.g., symmetry) for known particles and violate these constraints for nonexistent ones.

Finally, like most other models of scientific discovery, BR-4 ignores the interactions that occur among different researchers. Scientists cooperate along some dimensions, with theorists passing on predictions to experimentalists, who in turn report their observations to theorists. They also compete in developing theories to explain new findings, in discovering evidence for predicted events, and by noting errors in others' reasoning. The history of particle physics is rich in examples of such interactions, and we believe that some revisions to BR-4 will let us model some of them. In particular, we plan to assign different facets of the system's domain knowledge to different agents, which would communicate through a common representation; we will also let different agents explore different branches when search suggests alternative solutions.

5. Concluding Remarks
In this paper we presented BR-4, an abstract computational model of scientific discovery. We examined the system's behavior on three problems from particle physics, showing that it can replicate, though in a schematic way, important steps in the historical development of this field, some of which were considered major discoveries when first introduced. In particular, BR-4 proposes the existence of the neutrino to avoid violating conservation of spin, it invents baryon and lepton numbers to explain the absence of reactions involving proton decay, and it postulates electron and muon numbers to rule out unobserved neutrino reactions. In addition, the system can determine appropriate quantum values for each particle, and it can predict the reactions implied by a set of particles and quantum properties.

The BR-4 model accomplishes these feats using simple processes that play a central role in many aspects of human cognition. The system employs four basic operators for determining property values, creating new properties, positing new particles, and predicting reactions. Moreover, it uses consistency and completeness constraints to selectively apply these operators, and it incorporates depth-first control scheme to carry out search when necessary. The simplicity of these mechanisms, and their similarity to other processes observed in human behavior, suggest that one can explain some aspects of scientific creativity in similar terms.

References
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Karp, P. (1990). Hypothesis formation as design. In Shrager, J., and Langley P., eds., Computational models of scientific discovery and theory formation. Morgan Kaufmann, San Mateo, CA.

Klahr, D. (1994). Extended abstract: Children, adults and machines as discovery systems. Machine Learning, 14, 313-320.

Kocabas, S. (1991). Conflict resolution as discovery in particle physics. Machine Learning, 6 , 277-309.

Kocabas, S. (1992). Elements of scientific research: Modeling discoveries in oxide superconductivity. Proceedings of the ML 92 Workshop on Machine Discovery. Aberdeen, Scotland. (pp. 63-70).

Kocabas, S. (1993). Elements of Scientific Creativity. In Technical Report: Artificial Intelligence and Creativity . AAAI Press, pp. 39-45.

Kocabas, S. (1994). Goal directed discovery and explanation in particle physics. In Working Notes: Goal Driven Learning, AAAI Spring Symposium Series. (pp. 54-61).

Kulkarni, D. and Simon, H. (1988). The processes of scientific discovery. Cognitive Science, 12, 139-175.

Langley, P., Simon, H. A., Bradshaw, G. L., & Zytkow, J. M. (1987). Scientific discovery: Computational explorations of the creative processes. Cambridge, MA: MIT Press.

Ng, ?. and Mooney, ? (199?). ...

O'Rorke, P., Morris, S. and Schulenburg, D. (1990). Theory formation by abstraction. In Shrager, J., and Langley P. eds. Computational models of scientific discovery and theory formation. Morgan Kaufmann, San Mateo, CA.

Rajamoney, S.A. (1990). A computational approach to theory revision. In Shrager, J., and Langley P., eds., Computational models of scientific discovery and theory formation. Morgan Kaufmann, San Mateo, CA.

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Shrager, J. and Langley, P. Computational approaches to scientific discovery.In Shrager, J., and Langley P., eds., Computational models of scientific discovery and theory formation. Morgan Kaufmann, San Mateo, CA.

Tweney, R.D. (1990). In Shrager, J. and Langley, P. (eds.) Computational Models of Scientific Discovery and Theory Formation. Morgan Kaufmann, San Mateo, CA.

Valdes-Perez, R. E. (in press). Discovery of conserved properties in particle physics: A comparison of two models. Machine Learning.

Valdes-Perez, R. E., Zytkow, J. M., & Simon, H. A. (1993). Scientific model building as search in matrix spaces. Proceedings of the Eleventh National Conference on Artificial Intelligence (pp. 472-478). Washington, DC: AAAI Press.

Zytkow, J.M. and Simon, H. (1986). A theory of historical discovery: The construction of componential models. Machine Learning, 1, 107-137.

Goal Directed Discovery and Explanation in Particle Physics

GOAL DIRECTED DISCOVERY AND EXPLANATION
IN PARTICLE PHYSICS
Sakir Kocabas

Department of Artificial Intelligence
Tubitak - MRC, PK 21 Gebze, Turkey

Abstract:
This paper describes a goal directed discovery system, TREV, which models the disvery of certain quantum properties and conservation laws by physicists between 1920 and 1960. The program is directed by completeness and consistency constraints, and has the capability of explaining its knowledge state by these constraints. TREV is capable of formulating new elementary particles and particle reactions, and proposing observations to test their existence. According to the results of such observations, the program can revise its knowledge base (e.g. its hypotheses about the particles), until it achieves a consistent and complete theory of its domain.

1. Introduction
Goal directed discovery has been the focus of attention by several researchers in the last ten years, and a number of computational models with different capabilities have been developed. Among these systems, BACON (Langley, Simon, Bradshaw & Zytkow, 1987), has the capabilities of data collection, quantitative reasoning and hypothesis formation; IDS (Nordhausen & Langley, 1993) and FAHRENHEIT (Zytkow, 1987) have the features of data collection, qualitative and quantitative reasoning, and hypothesis formation; GLAUBER (Langley, et al., 1987), concept formation and the discovery of qualitative laws; STAHL (Zytkow & Simon, 1986), STAHLp (Rose & Langley, 1986), REVOLVER (Rose & LANGLEY, 1986), concept formation (i.e., the componential models of chemical substances or quark compositions of elementary particles) and theory revision; MECHEM (Valdes-Perez, 1992) discovery of reaction pathways; AbE (O'Rorke, Morris & Schulenburg, 1990), theory formation, explanation and theory revision by using qualitative schemas; GALILEO (Zytkow, 1990), theory formation; KEKADA (Kulkarni & Simon, 1988), goal selection, hypothesis formation, experiment design, and expectation setting; COAST (Rajamoney, 1990) and ECHO (Thagard, P. and Nowak, G., 1990), theory formation, theory revision and paradigm shifts by qualitative models; and BR-3 (Kocabas, 1991), theory formation and theory revision.

The subject of this paper is a goal directed discovery model TREV, with the capabilities of theory formation, experiment design, data acquisition, explanation, and theory revision. Before we describe the system and its behavior, it is appropriate to present some background information about its task domain, particle physics.

1.1 The Domain of Particle Physics

Until the last decade of the 19th century, material substances were thought to be consisting of indivisible atoms. Towards the end of that century, experiments with cathode ray tubes revealed the first elementary particle (the electron), which was to be identified as one of the basic components of an atom. Early in the 20th century, other elementary particles, the proton and the neutron were discovered. Later, observations on cosmic rays revealed a number of other particles such as the muon, pion, kaon, the neutrinos and the lambda particles. There are now well over a hundred elementary particles known, some of which are listed with their quantum properties in Table 1. Most of these particles are unstable, and quickly decay into a series of lighter and more stable particles such as the electron and neutrino, and into gamma rays. For example, a neutron decays to produce a proton, an electron and an antineutrino; and a pion decays into an antimuon and a neutrino:

n --> p + e + /nu
pi --> /mu + nu.
Particles also interact with one another under natural and experimental conditions, producing other elementary particles or gamma radiation. These reactions are called "particle transmutations". An example to such interactions is the high-energy electron-proton collision, which produces a neutron and a neutrino:

e + p --> n + nu.

The theoretical possibility of such particle reactions depend on a series of quantum conservation laws. According to these laws, quantum properties such as spin, lepton number, electrical charge, baryon number, strangeness, energy, and momentum are conserved in particle decays and collisions. However, some quantum properties may not be conserved in certain particle reactions, (e.g., the strangeness property is not conserved in weak interactions.)

Table 1. Some elementary particles and their quantum properties. With the exception of gamma, each particle has an antiparticle with opposite quantum values. The antiparticles are indicated with a '/' in the text (e.g. as in /n for anti-neutron).


----------------------------------------------------------------
electrical lepton baryon spin strangeness
charge number number
----------------------------------------------------------------
gamma 0 0 0 1 0
nu 0 1 0 1/2 0
mu -1 1 0 1/2 0
tau -1 1 0 1/2 0
e -1 1 0 1/2 0
pi 1 0 0 0 0
pi0 0 0 0 0 0
k 1 0 0 0 1
k0 0 0 0 0 1
p 1 0 1 1/2 0
n 0 0 1 1/2 0
----------------------------------------------------------------

1.2 Theory Development in Particle Physics

The earliest known laws about elementary particle reactions were the energy and charge conservation laws. The law of the conservation of charge can be stated as follows: The sum of the charges of the initial particles entering a reaction is equal to the sum of the charges of the final particles. The following reactions conserve electrical charge and have been "observed" by physicists:

p + p --> p + n + pi
pi0 --> gamma + gamma

where p, n, pi, pi0, and gamma designate the proton, neutron, pion, pion-zero and gamma particles respectively. It has been known since early this century that the proton and electron have opposite and unit electrical charges. The neutron has been known to be unstable, decaying into a proton, an electron, and an antineutrino in what is called "beta decay", or

n --> p + e + /nu
but a proton decay has never been observed, and the stability of this particle had puzzled the physicists. Why does it not decay into lighter particles? Reactions such as

p --> pi + pi0
p --> /e + gamma

never happen despite the fact that they apparently obey the charge conservation law. A theoretical framework based only on the charge conservation law would not be capable of explaining the absence of these reactions. In other words, such a theory would be incomplete concerning particle reactions.
The discrepancy between the theoretically valid and physically observable reactions was a conflict that had to be resolved. Physicists resolved these conflicts by postulating new quantum properties and conservation laws, so that theoretically valid but physically unobservable reactions were rendered theoretically invalid by these laws (see, Omnes, 1970; Griffiths, 1987). In this way the absence of these reactions were explained by their violation of the conservation of the new quantum property. The next problem was to find the quantum value distribution of the new property over the elementary particles.

=====================================
To illustrate how such conflicts were resolved, let us consider a reaction which conserves electrical charge but has not been observed

p --> pi + pi0.

Let us assume that this reaction violates the conservation of a new property (e.g., the "protonic charge"). Now, if we arbitrarily assign the new charge value to the proton as one and assume that the other particles, pi and pi0, do not have this charge (i.e., they both have zero protonic charge), then the reaction would be unbalanced by the new charge (i.e., 1 =/= 0 + 0). This would explain why the reaction had never been observed. Nevertheless, the value set [1,0,0] is not the only one that makes the reaction unbalanced, as the values [0,1,1], [0,1,0], [0,0,1] and [1,1,1] produce the same effect.
On the other hand, the new quantum values make some observed reactions unbalanced, as in

p + p --> p + n + pi
p + /pi --> n + pi0

These reactions conserve electrical charge, but not the "known" values of the new charge. This can be seen by substituting the protonic charge values:

1 + 1 = 1 + n + 0
1 + /pi = n + 0

This suggests that some of the other particles in these reactions must have nonzero protonic charge. Here, if we assign the protonic charge value of one to the neutron and zero to /pi, the reactions would be balanced. However, other valid and observed reactions may conflict with the assigned values, and we may have to revise some of the assumptions about the protonic charge values of particles accordingly.

+++++++++++++++++++
TREV, like its predecessor BR-3 (Kocabas, 1991) rediscovers the quantum properties in the same way as explained above. As the program's goal is to achieve a consistent and complete knowledge state, it postulates new hypotheses, and revises its domain knowledge until it achieves its goal state. In this way TREV models the discoveries of the lepton, baryon, electron, and muon number properties in particle physics. Apart from its theory formation and theory revision capabilities, the program has also the ability of proposing experiments and providing explanations for its assumptions about its domain objects.

In the remaining part of this paper we first present an overview of the system, and describe its behaviour in modeling the discoveries of the quantum properties, in proposing experiments, and in providing explanations. This is followed by a comparative discussion on the system's research goals, knowledge representation, theory revision and search methods, and its generality. The paper concludes with a summary of the results.

2. The System's Knowledge Representation and Behavior
The program uses a structured knowledge representation similar to qualitative schemas as in AbE (O'Rorke et al, 1990) and the other recent discovery models. This structured representation facilitates the system's identification of problem states such as incompleteness and inconsistency. Therefore we begin with describing the knowledge representation methods of TREV in some detail.

2.1 Knowledge Representation

TREV's knowledge organization distinguishes descriptive and prescriptive knowledge. The former type of knowledge is represented as frames, and the latter as a series of operators and functions. The program has nine operators which are named as follows: 'evaluate', 'check-consistency', 'check-completeness', 'postulate-properties', 'revise-hypotheses', 'find-quantum-values', 'formulate-new-particles', 'formulate-virtual-particles', and 'formulate-reactions'. The program also has a similarity based learning (SBL) module.
The main data items of TREV are elementary particles and their reactions. Both are represented as frames in the system's knowledge base. Particle frames include the name of the particle, the quantum properties and their values. The general form of a particle frame is as follows:

frame: P
class = particle
q1 = v1
q2 = v2
...
qn = vn.

where P is the name of the particle, q1,...,qn the quantum properties, and v1,...,vn the corresponding quantum values, which can be -1, 0, or 1.
Particle reactions are represented in a similar way, this time containing information about the reactions, such as the particles involved, the reaction conditions, the physical status of the reaction, and its validity under the current theory. The general form of a particle reaction frame is as follows:

frame: reaction
class = physical event
actual status = A
logical status = L, logical-status(N,L)
reactants = R
products = P
active properties = Q, active-properties(N,Q)
reactants properties = Rp, reactants-properties(Q,Rp)
products properties = Pp, products-properties(Q,Pp)
conditions = (Rp = Pp) or (Rp =/= Pp)

where A indicates whether the reaction has been physically observed or unobserved, and L indicates whether the reaction is valid or invalid under the current theoretical knowledge of the system. R and P are the lists of the particles involved in the reaction as the reactants and the products respectively. Q indicates the vector of quantum properties that play an active role in the reaction, while Rp and Pp are the quantum value vectors of the reactants and the products. Normally, particle reactions are added to the program's knowledge base (e.g. for the reaction n -> p + e + /nu) as follows:

frame: r1
class = reaction
actual status = observed
reactants = [n]
products = [p, e, /nu].

Such input reaction frames are then transformed into the form below by inheritance from the parent frame:

frame: r1,
class = reaction
actual status = observed
logical status = valid
reactants = [n]
products = [p, e, /nu]
active properties = [q0, q1]
reactants properties = [1, 0]
products properties = [1, 0]
conditions = {[1,0] = [1,0]}.

The amended slots are added after their values are calculated by the 'evaluate' operator.
TREV has two operators, 'check-consistency' and 'check-completeness', which can identify the problem states (inconsistency and incompleteness) about reactions.

The 'check-consistency' operator can decide whether the information in a reaction frame is consistent or inconsistent with the system's knowledge, by the following rules:

If R is a reaction,
and its actual status is o b s e r v e d,
and its logical status is v a l i d,
then R is consistent with the system's knowledge base.

If R is a reaction,
and its actual status is o b s e r v e d,
and its logical status is i n v a l i d,
then R is inconsistent with the system's knowledge base.

The check-completeness operator on the other hand, can also decide whether a reaction is explainable within the system's current knowledge, i.e., why the reation is physically observable or unobservable. In other words, the program can decide whether its knowledge concerning a particle reaction is complete or incomplete. The completeness rules are as follows:

If R is a reaction,
and its actual status is u n o b s e r v e d,
and its logical status is i n v a l i d,
then the system's knowledge base is complete regarding R.

If R is a reaction,
and its actual status is u n o b s e r v e d,
and its logical status is v a l i d,
then the system's knowledge base is incomplete regarding R.

The program checks its knowledge about reactions for consistency and completeness every time it is presented with a new set of data, and tries to achieve a consistent and complete knowledge state. In this, TREV uses a a control structure employed by its predecessor, BR-3 (Kocabas, 1991). Figure 1 summarizes the system's control structure. Accordingly, TREV first checks for consistency by using the above rules over its reaction frames, and reports inconsistent reactions to a message list. Inconsistent reactions are observed reaction that do not conserve a certain quantum property in the program's knowledge base.

An inconsistency report in the message list activates the 'revise-hypotheses operator'. This operator modifies the system's knowledge about the particles' quantum property values by first turning the inconsistent reactions into algebraic equations and finding sets of alternative quantum values for the particles appearing in these reactions. Since there are only three possible quantum values, namely -1, 0 and 1, modifications alternate between these values. Each vallue set is tried until the consistency constraints are satisfied.

On the other hand, after consistency has been achieved, but TREV cannot explain why a certain unobserved particle reaction is impossible, the program posts an incompleteness message to the message list. This in turn, activates the 'postulate-property' operator, which postulates a new quantum property. The program adds the new quantum property to a new slot in the particle frames with the default values of zero.

The 'find-quantum-values' operator turns the unobserved reaction formula into an algebraic inequality, and finds a set of quantum values for the particles in the formula. E.g. for the unobserved reaction p --> /e + gamma, the inequalities

0 =/= 0 + 1
0 =/= -1 + 0
1 =/= 0 + 0
1 =/= -1 + 0
1 =/= -1 + 1

are generated by the program. Each of these inequalities represent a set of quantum values for the new property, which enable TREV to explain the absence of the reaction. The first quantum value set (p=0, /e=0, gamma=1) is assigned to the particles first. However, the new values must be consistent with the system's knowledge of elementary particles and their observed reactions. To secure this, the quantum values for the new property are assigned to other particles, such that its conservation is satisfied in the observed reactions. The check-consistency operator checks if the new values are consistent, and the revise-hypotheses operator revises them as necessary. This cycle continues until the system achieves a consistent and complete knowledge state.

inconsistent revise check
knowledge ---> hypotheses ---> consistency
state and completeness


incomplete postulate find check
knowledge ---> new ---> quantum ---> consistency
state properties values


consistent and
complete ---> stop.
knowledge state

Figure 1. TREV's general control structure in the discovery of
quantum properties.

2.2 Formulation of New Particles

The program can define new particles by making modifications on the values of quantum property slots of existing particle frames. For example, from the neutron's frame

frame: n (neutron)
class = particle
q1 = 0 (electrical charge)
q2 = 0 (lepton number)
q3 = 1 (baryon number)

a new particle can be defined by changing the q1 value to -1 to obtain
the particle

frame: p1 (proposed particle)
class = proposed particle
q1 = -1 (electrical charge)
q2 = 0 (lepton number)
q3 = 1 (baryon number)

which, incidentally corresponds to anti-proton. The program proposes to make observations to check whether such postulated particles exist in nature. The important point about this exercise is that certain quantum property combinations never exist (e.g. particles having nonzero baryon and lepton values at the same time.) In fact, this observation had led to the development of the quark theory in particle physics in the 1960s.

After observations, if the proposed particle has been decided not to exist in nature then it is recorded as nonexistent particle e.g. as

frame: np1
class = nonexistent particle
q1 = v1
q2 = v2
q3 = v3

From its accumulated knowledge about existing elementary particles, TREV can construct hypotheses about the nonexistence of certain quantum value combinations, by an inductive method called exclusion based learning (Kocabas, 1989). These hypotheses state that particles with certain quantum property value combinations cannot exist. TREV can modify its exclusion hypotheses in view of the new knowledge about elementary particles. As soon as a new particle frame is created, the program checks its exclusion hypotheses to decide if the quantum values of the particle contradicts a hypothesis. If it does, the individual hypothesis is removed.
The exclusion hypotheses are added to the system's knowledge base as frames:

frame: ep1,
class = excluded q-composition
q1 = v1
q2 = v2
q3 = #

which means that the quantum values v1 and v2 for the properties q1 and q2 respectively, cannot be possessed by an elementary particle.

2.3 Formulation of Virtual Particles and New Reactions

The program formulates particle decays and collisions by first defining a set of 'virtual' particles. These are formulated simply by adding the vectors of quantum property values of two or three particles. An example to such virtual particles is the one that is formulated by adding the quantum values of the proton [1,0,1] and electron [-1,1,0], resulting in a proton-electron virtual particle with the quantum values of [0,1,1].

proton electron (proton-electron)

[1,0,1] + [-1,1,0] = [0,1,1]

In this way, a virtual particle with zero electrical charge, and with lepton and baryon numbers of 1 is defined. Such virtual particles are used in constructing particle decay and collision reactions. One such possible construction can be a neutron decay:

n --> p + e

which, incidentally, is not a valid reaction, because it does not conserve the quantum values of lepton property, as quantum value vectors of the reactants and products are not equal, i.e., [0,1,0] =/= [0,1,1]. On the other hand, the reaction, which is obtained by using the neutron and the virtual particle proton-electron- antineutrino (p,e,/nu),

n --> p + e + /nu


is a valid and observed reaction as it conserves all the three quantum properties, electrical charge, lepton and baryon numbers with the quantum value vectors of both sides being equal, i.e [0,1,0] = [0,1,0].

Testing the reactions proposed by TREV may lead to the discovery of new quantum properties. If a proposed reaction is valid by the program's knowledge of quantum values, but cannot be observed, then this creates an incompleteness problem for the program. As has been described above, in such cases TREV postulates a new quantum property and tries to find a consistent and complete set of values for particles regarding the new property.

2.4 TREV's Methods of Explanation

The program uses its structured knowledge representation for producing explanations about the objects and events of its domain. Explanations are provided when the system is in a consistent and complete knowledge state.
The program can explain why a certain proposed particle reaction is consistent or inconsistent with the system's knowledge about particle physics. In this type of explanations, TREV uses the definition of consistency over the reaction in question.

The consistency (or validity) of a certain proposed reaction is explained by proving that the reaction conserves the quantum values that the program knows. If the reaction does not conserve these quantum values, then it is not inconsistent (or invalid). Consistency (or validity) of a reaction can easily be decided by checking its 'logical status' slot, or by calculating the quantum value vectors of the reactant and the resultant particles and by comparing them. For example, the reaction n --> p + e + /nu is consistent because the 'actual state' slot of the reaction's frame says that the reaction has been observed, and the 'logical status' slot says it is valid. If the reaction frame does not have such a slot, then the 'check-validity' operator fires, which in turn finds if the reaction conserves the known quantum properties.

TREV can explain why a certain reaction is not observable by proving that it violates the conservation of a quantum property that it knows. Also, by using its completeness constraints, the program can explain why the impossibility of a certain unobserved reaction is or is not explainable within the program's domain theory. When the program cannot explain the absence of such a reaction by its domain theory, then it concludes that its knowledge about elementary particles is incomplete concerning the unobserved reaction. As has been described above, TREV resolves such problem states by postulating a new quantum property.

On the other hand, the program can also explain why there can be no particles with a certain set of quantum properties, by using its exclusion hypotheses for such explanations. For example, the exclusion hypothesis

frame: ep1,
class = excluded q-composition
q1 = 1
q2 = 1
q3 = #

explains why there cannot be a particle with the quantum values of q1=1, q2=1, and q3=0.
The system's explanatory power increases as it discovers new quantum properties, and as the particle descriptions become more detailed by including new quantum property slots and values.

TREV can learn to explain consistency and completeness by its similarity based learning (SBL) module. In learning a concept (e.g. 'consistent'), the SBL module compares the positive instances of the concept (i.e. valid and observed reactions), and creates the definition of the concept. The system's consistency and completeness rules are created in this way.

3. Discussion on the System's Methods
TREV is a system that combines several features of a discovery model. Every discovery system, by definition, must have the ability to learn. The program has three distinct types of learning ability, namely inductive learning and learning by discovery. As described above, TREV learns its consistency and completeness constraints by similarity based learning, and its exclusion hypotheses, by exclusion based learning methods. The program also constructs its domain theory with its ability to learn by observation and by discovery. The former involves the formulation of new particles and reactions, and their subsequent comparison with the physical world. The latter takes place by postulating new quantum properties and assigning a set of corresponding quantum values to the particles.

An important feature of a discovery model is theory development, which itself can be divided in two tasks as theory formation and theory revision. TREV extends its domain theory by using its learning and discovery abilities, by adding exclusion hypotheses, by formulating its consistency and completeness constraints, and by postulating new quantum properties when faced with an incomplete knowledge state. When it is faced with an inconsistent knowledge state, the program revises its domain knowledge (i.e. knowledge about particles and their reactions) by using its consistency constraints together with general algebraic constraints.

In its theory development and theory revision activities based on the consistency and completeness constraints, the program works in a coordinated way. However, the system's other task operators work independently and in an uncoordinated way. For example, the 'evaluate', 'formulate-new-particles', 'formulate-virtual-particles', and 'formulate-reactions' operators are fired by an external agent (e.g. a user) independently. Similarly, explanation generating functions of the system are called on user demand and for specific purposes, such as in explaining why a particular is unobservable.

Also, the operators which formulate new particles and reactions are not constrained by domain dependent and general constrains. Hence, they operate in a relatively large search space. As a result, these operators can formulate uninteresting domain objects as well as the interesting ones.

TREV's explanation functions take advantage the system's structural knowledge representation. The explanations provided are simple, and do not go deeper into the system's domain theory. However, the program can be improved in this direction.

The program's ability to fromulate new objects means that it has the ability to propose observations to decide whether the formulated objects (i.e. elementary particles and reactions) exist in nature. Observation results are entered by the 'user'. There are a few discovery models, such as IDS (Nordhausen & langley, 1993) and FAHRENHEIT (Zytkow, 1987) that can directly receive data from their physical environment. However, experimental setup is rather complex for any direct data acquisition in the domain of TREV.

The program has two types of theory revision capability. One is based on using the consistency constraints, and the other is theory revision by observational evidence.

Another shortcoming of the program is that the theory formation and revision operators fired by a rule set whose conditions are determined by the message list. In other words, the control rules are hardwired, though an explanation based learning method could be used to learn such rules. We will address this problem in the future versions of the program.

4. Conclusions
One important problem in artificial intelligence is building models that integrate different methods of representation and learning. We have described a discovery system, directed by completeness and consistency constraints, with the capabilities of theory formation and theory revision, and with the ability of explaining its knowledge state by its domain constraints. The system is capable of formulating new elementary particles and particle reactions, and proposing observations to test their existence. The program has a certain degree of integration in its representation, learning and discovery methods, which can be further improved.

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