From: AAAI Technical Report SS-94-02. Compilation copyright © 1994, AAAI (www.aaai.org). All rights reserved.
GOAL DIRECTED DISCOVERY AND EXPLANATION
IN PARTICLE PHYSICS
SAKIR KOCABAS*
Department
of Artificial Intelligence
Tubkak - MRC,PK21 Gebze, Turkey
Email: uckoca@tritu.bitnet
Abstract:This paper describes a goal directed discoverysystem, TREV,whichmodelsthe disvery of certain
quantumpropertiesand conservationlawsby physicists in thi.~ century. Theprogramis directed by consistency
and completenessconstraints, and has the capability of improvingand revising its domaintheory, and of
explainingits knowledge
state by these constraints. TREV
is capableof formulatingnewelementaryparticles
and particle reactions, and proposingobservations to test their existence. Theprogramcan also generate
exclusionhypotheses,and can revise its knowledgebase in accordancewith observationaldata.
1. Introduction
Thesubject of this paper is a goal directed discovery
model
TREV,with the capabilities of theory formation,
Computationalmodelingof discovery has beenthe focus
experimentdesign, data acquisition, explanation, and
of attention by several researchersin the last ten years,
theory
revision. Beforewedescribe the systemand its
and a numberof modelswith different capabilities have
been developed. Amongthese systems, BACON behavior, it is appropriate to present somebackground
informationaboutits task domain,particle physics.
(Langley, Simon, Bradshaw& Zytkow, 1987), has the
capabilities of data collection, quantitativereasoningand
1.1. The Domain of Particle Physics
hypothesis formation; IDS(Nordhausen& Langley,1993)
and FAHRENHEIT
(Zytkow, 1987) have the features
data collection, qualitative and quantitative reasoning, Until the last decadeof the 19th century, material substanceswerethoughtto be consisting of in.visible atoms.
and hypothesis formation; GLAUBER
(Langley, et al.,
Towards
the end of that century, experiments with
1987), conceptformationandthe discoveryof qualitative
laws; STAHL
(Zytkow& Simon, 1986), STAI-ILp(Rose cathoderay tubes revealed the first elementaryparticle
(the electron), whichwasto be identified as one of the
& Langley, 1986), REVOLVER
(Rose & Langley, 1986),
of an atom. Early in the 20th century,
concept formation and theory revision; MECHEM basic components
other
elementary
particles, the proton and the neutron
(Valdes-Perez, 1992) discovery of reaction pathways;
were discovered. Later, observations on cosmic rays
AbE(O’Rorke, Morris & Schulenburg, 1990), theory
formation, explanation and theory revision; GALILEO revealed a numberof other particles such as the muon,
pion, kaon,the neutrinosand the lambdaparticles. There
(Zytkow, 1990), theory formation; KEKADA
(Kulkarni
are nowwell over a hundredelementaryparticles known,
& Simon,1988), goal selection, hypothesis formation,
experiment design, and expectation setting; COAST someof whichare listed with their quantumproperties in
(Rajamoney, 1990) and ECHO
(Thagard, P. and Nowak, Table1. Mostof these particles are unstable, andquickly
G., 1990), theory formation,theory revision and paradigm decayintoa series of lighter andmorestable particles such
as the electron and neutrino, and into gamma
rays. For
shifts by qualitative models;and BR-3(Kocabas,1991),
example,a neutron decaysto producea proton, an electheory formationand theory revision.
* Also at: ITU,Faculty of SpaceSciencesand Technology,Istanbul, Turkey
54
tron and an antineutrino; and a pion decays into an
antimuonand a neutrino:
Table1. Some
elementary
particlesandtheir quantum
properties.Withthe exception
of gamma,
eachparticle
hasanantiparticlewithopposite
quantum
values.The
antiparticlesare indicatedwith an overscore
in the text
(e.g. asin nfor anti-neutron).
Particles also interact with one another undernatural
and experimentalconditions, producingother elementary
particles or gamma
radiation. Thesereactions are called
"particle transmutations".Anexampleto suchinteractions ?
is the high-energyelectron-protoncollision, whichprodu- v
ces a neutron and a neutrino:
/~
r
e +p --- n+v.
e
Thetheoretical possibility of such particle reactions
dependon a series of quantumconservationlaws. Accordhagto these laws, quantumproperties such as electrical
charge, spin, lepton number,baryonnumber,strangeness,
energy, and momentum
are conserved in particle decays
and collisions. However,somequantumproperties may
not be conservedin certain reactions, (e.g., the strangeness propertyis not conservedin weakinteractions.)
1.2. TheoryDevelopment
in Particle Physics
The earliest knownlaws about elementary particle
reactions werethe energyand charge conservationlaws.
Thelaw of the conservation of charge can be stated as
follows: Thesumof the charges of the initial particles
entering a reaction is equal to the sumof the charges of
the final particles. Thefollowingreactionsconserveelectrical chargeand havebeendetected by physicists:
p+p ~p+n+~r
3to ~ y+y
where p, n, ~, ~o, and gsmmadesignate the proton,
neutron, pion, pion-zero and gammaparticles
respectively. It has been knownsince early this
century that the proton and electron have opposite
and unit electrical charges. The neutron has been
knownto be unstable, decaying into a proton, an
electron, and an antineutrino in what is called "beta
decay", or
n --,p
+e+v
55
Sro
K
Ko
p
n
electrical lepton baryon spin strangeness
charge number number
0
0
-1
-1
-1
1
0
1
0
1
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1/2
1/2
1/2
1/2
0
0
0
0
1/2
1/2
0
0
0
0
0
0
0
1
1
0
0
but a proton decay has never been observed, and the
stability of this particle had puzzled the physicists.
Reactions such as
p-~ ~r + Zro
p’-" e +?
never happendespite the fact that they apparently obey
the charge conservation law. A theoretical framework
based only on the charge conservation law could not
explain the absenceof these reactions. In other words,
such a theory wouldbe incompleteconcerningparticle
reactions.
Physicists resolved such problemsby postulating new
quantumproperties and conservationlaws, so that theoreticallyvalid but physicallyunobservable
reactions were
renderedtheoretically invalid by these laws (see, Omnes,
1970; Griffiths, 1987). In this waythe absenceof these
reactions wereexplainedby their violation of the conservation of the newquantumproperty. Thenext problem
was to find the quantumvalue distribution of the new
property over the elementaryparticles.
To illustrate howsuch conflicts wereresolved, let us
consider a reaction whichconserveselectrical chargebut
has not been observed
In the remainingpart of thi.~ paper wefirst present an
overviewof the system, and describe its behavior in
modelingthe discoveries of the quantumproperties, in
Let us assumethat this reaction violates the conservation proposing experiments, and in providing explanations.
This is followedby a discussionon the system’sresearch
of a newproperty(e.g., the "protoniccharge"). Now,if
arbitrarily assign the newchargevalue to the proton as
goals, knowledge
representation, theory revision and seoneand assumethat the other particles, ~ and ~0, do not
arch methods,and its generality. The paper concludes
have this charge (i.e., they both have zero protonic
with a summary
of the results.
charge), then the reaction wouldbe unbalancedby the
newcharge (i.e., 1 = / = 0 + 0). This wouldexplain why 2. The System’s Knowledge Representation
and Behavior
the reaction had never been observed. Nevertheless,
the value set [1,0,0] is not the only one that makesthe
The programuses a structured knowledgerepresentation
reaction unbalanced, as the values [0,1,1], [0,1,0],
similar to qualitative schemasas in AbE(O’Rorkeet al,
[0,0,1] and [1,1,1] produce the same effect. On the
1990) and the other recent discovery models. This
other hand, the new quantumvalues makesome obstructured representation facilitates the system’sidenserved reactions unbalanced, as in the following
tification of problemstates such as incompletenessand
reactions:
inconsistency. Therefore webegin with describing the
p+p ...,
p+n+~
knowledge representation methods of TREVin some
p +~ --~
n +~o
detail.
Thesereactions conserveelectrical charge, but not the
"known"values of the newcharge. This can be seen by
substituting the protonic chargevalues:
2.1. KnowledgeRepresentation
TREV’s
knowledgeorganiTation distinguishes descriptive and prescriptive knowledge.The former type of
1+1=1+n+0
knowledge
is representedas frames, and the latter as a
l+~=n+O
series of operators and functions. Theprogramhas nine
operators whichare namedas follows: evaluate, checkThis suggeststhat someof the other particles in these
consistency, check-completeness, postulate-propertreactions must havenonzeroprotonic charge. Here, if we ies, revise-hypotheses, find-quantum-values,
formulate-virtual-particles,
assign the protonie chargevalue of oneto the neutronand formulate-new-particles,
zero to ~r, the reactions wouldbe balanced. However, and formulate-reactions. The programalso has a
other valid and observed reactions may conflict
similarity
based learning (SBL)module.
with the assigned values, and we mayhave to revise
The maindata items of TREV
are elementaryparticles
some of the assumptions about the protonie charge
andtheir reactions. Bothare representedas framesin the
values of particles accordingly.
system’s knowledgebase. Particle frames include the
TREV,like its predecessor BR-3(Kocabas, 1991)
nameof the particle, the quantumproperties and their
values.Thegeneralformof a particle frameis as follows:
rediscovers the quantumproperties in the same wayas
explainedabove. As the program’sgoal is to achieve a
consistent and completeknowledgestate, it postulates
frame: P (frame name)
newhypotheses,andrevises its domainknowledge
until it
class = particle
achieves its goal state. In this wayTREV
modelsthe
ql = vl
discoveries of the lepton, baryon, electron, and muon
q2 = v2
numberproperties in particle physics. Apart from its
theory formationand theory revision capabilities, the
qn = vn.
programalso has the ability of proposingexperimentsand whereP is the nameof the partide, ql,...,qn the quantum
providing explanations for its assumptions about its
properties, and vl,...,vn the corresponding quantum
domainobjects.
values,whichcan be -1, 0, or 1.
56
Particle reactionsare representedin a similar way,this
time containinginformationabout the reactions, such as
the particles involved,the reaction conditions,the physical status of the reaction, andits validity underthe current
theory. Thegeneralformof a particle reaction frameis 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 ;~
whereAindicates whetherthe reaction has been physically observedor unobserved,and L indicates whetherthe
reaction is valid or invalid underthe current theoretical
knowledgeof the system. R and P are the lists of the
particles involvedin the reaction as the reactants andthe
productsrespectively. Qindicates the vector of quantum
properties that play an active role in the reaction, while
Rpand Pp are the quantumvalue vectors of the reactants
andthe products. Normally,particle reactions are added
to the program’sknowledge
base (e.g. for the reaction
-,p + e + v) as follows:
frame:rl
class = reaction
actual status = observed
reactants = [n ]
products= [p, e, v ].
Suchinput reaction framesare then transformedinto the
formbelowby the ’evaluate’operator acting on the parent
The amendedslots are added after their values are
calculated by the ’evaluate’ operator.
2.2. Theory Formation and Revision
TREV
has two operators for consistency and completeness checks: check-consistency and check-completeness. These operators can identify the problemstates
(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
followingrules:
If Ris a reaction,
andits actual status is observed,
andits logicalstatus is valid,
thenthe system’sknowledge
of Ris consistent.
If Ris a reaction,
and its actual status is observed,
andits logicalstatus is invalid,
then the system’sknowledge
of R is inconsistent.
The check-completeness
operator on the other hand,
can also decidewhethera reaction is explainablewithin
the system’scurrent knowledge,i.e., whythe reation is
physically observableor unobservable.In other words,
the program can decide whether its knowledgeconcerning a particle reaction is completeor incomplete.
The completenessrules are as follows:
If Ris a reaction,
andits actualstatus is unobserved,
andits logicalstatusis invalid,
then the system’sknowledge
of Ris complete.
If Ris a reaction,
and its actual status is unobserved,
andits logicalstatus is valid,
then the system’s knowledge
of R is incomplete.
frame:
frame: rl,
class = reaction
actual status = observed
logical status -- valid
reactants = [n ] m
products= [p, e, v ]
active properties = [q0, ql]
reactants properties = [1, 0]
products properties = [1, 0]
conditions= {[1,0] = [1,0]}.
The programchecks its knowledgeabout reactions for
consistency and completenessevery time it is presented
with a newset of data, and tries to achievea consistent
and complete knowledgestate. In this, TREV
uses a a
control structure employedby its predecessor, BR-3
(Kocabas,1991). Figure 1 summarizesthe system’s con-
57
trol structure. Accordingly,TREV
first checksfor consistency by usingthe aboverules over its reaction frames,
andreports inconsistent reactions to a messagelist.
Aninconsistencyreport in the messagelist activates the
revise-hypothesesoperator. This operator modifies the
system’s knowledgeabout the particles’ quantumproperty values by first turning the inconsistent reactions
into algebraic equations, and then by finding sets of
alternative quantumvalues for the particles appearing
in these reactions. Since there are only three possible
quantumvalues, namely -1, 0 and 1, modifications
alternate betweenthese values. Eachvalue set is tried
until the consistencyconstraints are satisfied.
Onthe other hand, after consistencyhas beenachieved,
ifTREVcannot explain whya certain unobservedparticle
reaction is impossible, the programposts an incompleteness messageto the messagelist. This in turn, activates
the postulate-property operator, which postulates a
new quantum property. The program adds the new
quantumproperty to a newslot in the particle frames
with the default values of zero.
The find-quantum-values operator turns the unobservedreaction formulainto an algebraic inequality,
and finds a set of quantumvalues for the particles
in
m
the formula. E.g. for the unobservedreaction p --,e +7,
the inequalities
0~0+1
0~-1+0
1¢0+0
1~-1+0
1¢-1+1
check
consistency
check
completeness
l
I
find quantum
values
I postulatenew
properties
I
Figure1. TREV’s
generalcontrol structurein the
discoveryof quantum
properties.
2.3. Formulation of NewParticles
The programcan define new particles by makingmoditications on the values of quantumproperty slots of
existing particle frames.For example,fromthe neutron’s
frame
frame: n (neutron)
class = particle
ql = 0 (electrical charge)
q2 = 0 (lepton number)
q3 = 1 (baryon number)
a newparticle can be definedby changingthe ql value to
-1 to obtain the particle
are generatedby the program.Eachof these inequalities
represent a set of quantumvalues for the newproperty,
whichenable TREV
to explain the absence of the reaction. Thefirst quantumvalueset (p = 0, e = 0, 7 = 1)
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 quantumvalues
for the newproperty are assigned to other particles,
such that its conservation is satisfied in the observed reactions. The cheek-consistency operator
checksif the newvalues are consistent, and the revisehypotheses operator revises them as necessary. This
cycle continues until the system achieves a consistent
and complete knowledgestate.
58
franle:
ppl (proposedparticle)
class = proposedparticle
ql = -1 (electrical charge)
q2 = 0 (lepton number)
q3 = 1 (baryon number)
which,incidentally correspondsto anti-proton. Theprogram proposes to makeobservations to check whether
such postulated particles exist in nature. Theimportant
point about this exercise is that certain quantum
property
combinationsnever exist (e.g. particles havingnonzero
baryonandlepton values at the sametime.) In fact, this
observation had led to the developmentof the quark
theoryin particle physicsin the 1960s.
After observations, if the proposedparticle has been
decided not to exist in nature then it is recorded as
nonexistentparticle e.g. as
In this way,a virtual particle withzero electrical charge,
and with lepton and baryonnumbersof 1 is defined. Such
virtual particles are used in constructingparticle decay
and collision reactions. Onesuch possible construction
can be a neutron decay:
frame: npl
class = nonexistentparticle
ql = vl
n’-*p+e
q2 = v2
which,incidentally,is not a valid reaction, becauseit does
q3 = v3
not conservethe quantumvalues of lepton property, as
Fromits accumulatedknowledgeabout existing elequantumvalue vectors of the reactants and products are
mentaryparticles, TREV
can construct hypothesesabout not equal, i.e., [0,1,0] = / = [0,1,1]. Onthe other hand,the
the nonexistenceof certain quantumvalue combinations, reaction, whichis obtainedby using the neutron and the
by an inductive methodcalled exclusion based learning
virtual particle proton-electron-antineutrino
(p,e,/nu),
(Kocabas,1989). These hypothesesstate that particles
with certain quantumpropertyvaluecombinationscannot
n--,,p+e+
v
exist. TREV
can modifyits exclusion hypothesesin view
of the newknowledge
about elementaryparticles. As soon is a valid andobserved
reactionas it conservesall the three
as a newparticle frameis created, the programchecksits
quantumproperties, electrical charge, lepton and baryon
exclusion hypothesesto decide if the quantumvalues of
numberswith the quantumvalue vectors of both sides
the particle contradicts a hypothesis.If it does, the inbeingequal, i.e [0,1,0] = [0,1,0].
dividual hypothesisis removed.Theexclusion hypotheses
Testing the reactions proposedby TREV
maylead to
are addedto the system’s knowledgebase as frames:
the discovery of newquantumproperties. If a proposed
reaction is valid by the program’sknowledge
of quantum
frame: epl,
values, but cannot be observed, then this creates an
class = excludedq-composition
incompleteness problem for the program. As has been
ql = vl
described above, in such cases TREV
postulates a new
q2 = v2
quantumproperty and tries to find a consistent and
q3=#
completeset of values for particles regarding the new
whichmeansthat the quantumvalues vl and v2 for the
property.
properties ql and q2 respectively, cannotbe possessedby
an elementaryparticle.
2.5. TREV’sMethodsof Explanation
2.4. Formulation
of Virtual Particles
and NewReactions
Theprogramformulatesparticle decaysand collisions by
first defining a set of "virtual" particles. Theseare
formulated simply by adding the vectors of quantum
property values of two or three particles. Anexampleto
such virtual particles is the one that is formulatedby
adding the quantumvalues of the proton [1,0,1] and
electron [-1,1,0], resulting in a proton-electronvirtual
particle with the quantum
values of [0,1,1].
proton electron (proton-electron)
I1,0,11+ I-l,l,0] = [0,1,11
59
Theprogramuses its structured knowledgerepresent~ition for producingexplanations about the objects and
events of its domain.Explanationsare providedwhenthe
systemis in a consistent and completeknowledge
state.
TREV
can explain whya certain proposed particle
reaction is consistent or inconsistent with the system’s
knowledgeabout particle physics. In this type of explanations, the programuses the definition of consistency
over the reaction in question.
The consistency (or validity) of a certain proposed
reaction is explainedby proving that the reaction conserves the quantumvalues that the programknows.If the
reaction does not conservethese quantumvalues, then it
is not inconsistent(or invalid). Consistency
(or validity)
of a reaction can easily be decidedby checkingits logical
status slot, or by calculating and comparingthe quan-
tuna value vectors of the reactant and the resultant
m
particles. For example, the reaction n ---p + e + v is
consistent because the actual state slot of the reaction’s
frame says tha.t 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 cheek-validity
operator fh-es, which in turn finds if the reaction conserves the known quantum properties.
TREV
can explain whya certain reaction is not observable by proving that it violates the conservation of a
quantumproperty that it knows. Also, by using its completeness constraints, the program can explain whythe
impossibility of a certain unobservedreaction is or is not
explainable within the program’s domain theory. When
the programcannot explain the absence of such a reaction
by its domaintheory, then it concludes that its knowledge
about elementary particles is incomplete concerning the
unobserved reaction. As has been described above,
TREVresolves 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: epl,
class = excluded q-composition
ql = 1
q2 = 1
q3 = #
explains whythere cannot be a particle with the quantum
values of ql = 1, q2 = 1, and q3 = 0.
The system’s explanatory powerincreases as it discovers
new quantumproperties, and as the particle descriptions
become more detailed by including new quantum property slots and values.
TREVcan learn its consistency and completeness constraints by its similarity based learning (SBL)module.
learning a concept (e.g. consistent), the SBLmodule
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.
60
3. Discussion
on the System’s
Methods
TREVis 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, namelyinductive 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 domaintheory with its ability to learn by
observation and by discovery. The former involves the
formulation of new particles and reactions, and their
subsequent comparisonwith the physical world. The latter
takes place by postulating new quantum properties and
assi,t, ning a set of corresponding quantumvalues 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. TREVextends its
domaintheory by using its learning and discoveryabilities,
by adding exclusion hypotheses, by formulating its consistency and completenessconstraints, and by postulating
new quantum properties when faced with an incomplete
knowledgestate. Whenit is faced with an inconsistent
knowledgestate, the program revises its domain theory
(i.e. knowledgeabout particles and their reactions)
using its consistency constraints together with general
algebraic constraints.
In its theory developmentand theory revision activities
based on the consistency and completeness constraints,
the program works in an integrated way. However, the
system’s other task operators work independently and in
an uncoordinatedway. For example,the oval uato, formulate-now-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 whya particular particle or reaction 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’sexplanation functions take advantage of 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 improvedin 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,
sueh as IDS (Nordhausen & langley,
1993) and
FAHRENHEIT
(Zytkow, 1987) that can directly receive
data from their physical environment. In the domain of
TREVhowever, experimental conditions are rather complex for any direct data acquisition.
The programhas two types of theory revision capability.
Oneis based on using the consistency constraints, and the
other is theory revision by observational evidence. The
former uses algebraic and domainconstrints, and therefore, is less general, whilethe latter is basedon observational results, abd therefore simpler and more general.
Another shortcoming of the program is that the theory
formation and revision operators are fired by a rule set
whose conditions are determined by the messagelist. In
other words, the control rules are hardwired, though an
explanation based learning methodcould be used to learn
such rules. Wewill address this problem in the future
versions of the program.
4. Conclusions
Oneimportant problemin artificial intelligence is buildhag modelsthat integrate different methodsof representation and learning. Wehave 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 knowledgestate
by its domain constraints.
The system is capable of
formulating new elementary particles
and particle
reactions, and proposing observations to test their existence. The programhas a certain degree of integration in
its representation, learning and discovery methods, which
can be further improved.
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