abstract introduction€¦ · synthesis in organic chemistry is difficult. it consists of creating...

Analogical reasoning: An organic chemistry

application

M. Py

5, France

FRAMENTEC-COGNITECH, 1 Place de la

coupole, 92084 Paris La defense, France

ABSTRACT

The purpose of this paper is to describe a formal framework able to reasonby analogy. It is constituted by two models, one from the French analogicalresearch group [6], the other from rational agent [26, 25]. The first definesthe notions used to reason by analogy. The second deals with knowledgemanagement by learning and verification. Our framework is validated bythe experimental results of the rational-agent prototype implemented on acomplex range (i.e. the synthesis of molecules in organic chemistry).

INTRODUCTION

Synthesis in organic chemistry is difficult. It consists of creating a moleculeaccording to a set of known reactions. A molecule can be considered asa coloured graph, and reactions as operators on graphs. To show thedifficulties of the synthesis problem, let us simplify it. If the moleculargraph contains n bonds, and if we suppose that we are able to synthetizeit by creating ra bonds, then there are Pnm possible solutions at the strate-gic level. Because the creations are ordered, the number of possible so-lutions is the number of permutations of m bonds selected from n ones:Pnm = n(n - 1) . . . (n - m + 1) = yr- There are others levels (political,

strategic, tactical. . . ) which increase the combinatory factor. To reduce it,the idea is to fit a previous synthesis of a similar molecule to the one wewant to synthetize. This is analogical reasoning.

Analogy is a frequently used method of reasoning. Metaphor and case-law are examples. When we have to solve a new problem, it is easy to

Transactions on Information and Communications Technologies vol 1, © 1993 WIT Press, www.witpress.com, ISSN 1743-3517

330 Artificial Intelligence in Engineering

search for a previous solved one. The method employed and the solutioncan be used to provide the solution to a new problem. This assumes thatwe are able to compare the two problems, and determine their similarities,the significance of the data, the dependencies between data and solutions,and the changes to be brought to the new solution from the previous one.These are essential notions that need to be defined.

Synthesis is related to chemical engineering by the different levels used:political and strategic. For instance, when a chemist wants to industriallysynthetize a molecule, he is concerned with easily attained temperatureconditions, cheap catalists, well managed reactions.... These are politicalrestrictions which are voiced in the system's language and which involvestrategic choices.

The purpose of this paper is to describe the formal framework usedto implement a prototype able to reason by analogy. We will see howthis reasoning method is useful in the synthesis of molecules in organicchemistry. The first section presents the analogical research group's model[6], the second one describes the rational agent's approach, and the thirddeals with our formal framework which makes use of both models. Althoughour framework is not dedicated to a particular range, all the different notionsare illustrated using organic chemistry synthesis.

ANALOGICAL REASONING

Several analogical reasoning models have been developed, such as the LeaSombe [27] (Lea Sombe is a collective name), Dedre Centner [15], Rogers P.Hall [17], John Wolstencroft [34], and finally the analogical research groupmodel [6], (There are many works on analogy that the reader can consult[1, 5, 4, 3, 7, 12. 14. 13. 16, 19, 18, 20. 22, 8. 28, 32, 33, 31, 30. 29. 21]), Theanalogical research group was composed of French teams interested in ana-logical reasoning. The collaborators are Daniel Coulon, Jean-Marie David(GRIN), Louis Bourrelly, Eugene Chouraqui, Joel Savelli (GRTC), Lau-rent Bruneau (CNET), J-F Bcisvieux, Brigitte Seroussi (INSERM), Chris-tel Vrain, Cheng-Ren Lu (LRI) and myself (LIRMM). The first four modelsare too general and (or) some important notions are missing (e.g. the LeaSombe's model presents analogical reasoning as a very general inferencerule. It uses the similarity notion without defining it ). We will present anduse the last one, which we consider to be the most complete.

The first part of our model is dedicated to knowledge representation.which is schematically portrayed in figure 1. The problem to solve is de-scribed in a universe. It is named target and noted UQ. The solved prob-lems are described in universes too. They are called bases and noted t/i(i — 1.... n). Problem data are noted A{ (i — 0.... n) and their solutions6i (i = 0,... n). Of course, BQ is unknown. Analogical reasoning uses three


Artificial Intelligence in Engineering 331

The previoussolved problems

One of thebest bases

The solution

The target

The data

The dependencyrelationshipThe unknownsolution

relationship

Figure 1: Knowledge representation

Let us suppose that we want to synthetizethe first molecule (on the left). We wantto find the industrial molecules whichcould be the starting molecules of the syn-

\[\ ••'^ ^ . thesis. We can do it by analogy. We areII / '' "•/. ' ^ 7 looking for the industrial molecules simi-

lar to the molecule to be synthetized (this isthe point of view).

Our prototype finds the ones presented on the right. The solid lines showwhere the industrial molecules match. Thus, to synthetize the molecule, weonly have to create the bonds printed with dotted lines, and keep the bondsprinted with solid lines. This information has to be added to the knowledge

(This is the reformulation of the universe).

Figure 2: An original example of the universe reformulation and of a point

of view

sorts of relationships:

• The dependency relationship (3. 3i (i = 0,... n),

• The mapping relationship between the basis and the target cv,

• The generalization relationship 7.

The dependency relationship determines both the relevant data to solve theproblem and the way in which the solution depends on the data.

Knowledge is produced by processes which are components of analogical

reasoning. These processes are:

• Reformulating the universe according to point of view (e.g.it might bethe choice between two theories, see figure 2),



One of thebest bases

We do not know the dependency func-tion DO and of course the solution BQ.We suppose that we are able to deter-mine the transferring function. Thedependency function D, of one of thebest bases is known. So to approxi-mate T>Q and BQ we have to apply thethree known functions.

Figure 3: Functions of analogical reasoning

* Identifying potential bases (i.e. searching for similar solved problems),

• Searching dependency relationships This can be done by knowledgeacquisition,

• Searching and setting up the mapping relationship,

• Transferring the knowledge from similar and previously solved prob-lems (i.e. the basis) to the one to solve (i.e. the target),

• Evaluating the inference.

In order to specify this model, we have added some definitions. There-fore analogical reasoning is equivalent to determination or approximationfunctions (see figure 3). Thus, functions D, correspond to dependency rela-tionships ,3i and T, T~* corresponds to knowledge transfers. Reasoning byanalogy means to determine or approximate the dependency function Do ofthe target by:

• transferring knowledge between the data of the target ylo and the dataof the basis Ai,

• using the dependency function D, between Ai and 5%,

• transferring knowledge between solutions Bi and BQ.

; o T

In order to do this, the following hypothesis needs to be made: ''thesefunctions exist and we can determine or approximate them" . This hypoth-esis expresses the fragility of analogical reasoning and demonstrates why aprocess which evaluates the inference is needed.



Synthesis planP T

Synthesis planP'

We want to solve the following problem by analogy: "how can we synthetizethe molecule AQ ? The dependency function DO and the solution BQ (i.e.

the synthesis plan) are not known.The best similar molecule (i.e. the basis A) has been determined.Matching is presented with solid lines (dotted lines otherwise).It can be seen that the target is totally involved in the basis. The synthesis

plan of this molecule is known.If it is chemically possible to convert AQ into A* then we have determinedby analogy a synthesis plan for AQ. The function T~* is a compound ofthe chemical reactions which convert AQ into A A is known. This is themethod used to make the synthesis plan. % is the synthesis plan of moleculeAi. T is the identity function. BQ is the result of the three functions on AQ.

Figure 4: An example of analogical reasoning

An example of analogical reasoning is given (see figure 4) in the range

of organic chemistry.However, this formal framework is always too general. For example, it

identifies a dependency relationship searching process without specifyingthe method. Since our objective is to have a system capable of learningdependencies, this needs to be explained. That is why we link our formalframework to another one: the rational agent [26, 25]. We will use thedifferent notions which have just been defined, and include the rationalagent's notions in order to enlarge our formal framework.

THE RATIONAL AGENTS

A rational agent (cf [26, 25]) manages its own knowledge by exchangingmessages with other agents. It is capable of using noisy data.

Its aim is to produce knowledge. To do this, it uses four basic processes:

• Abduction, which consists in determining what is frequently seen ona set of examples and rarely on a set of counter-examples. (It can beobserved that the rational agent's abduction is not classic. For moreinformation see [26, 25]),



• Induction, which produces hypotheses according to the results of ab-duction,

• Deduction, which is used to locate the induced hypothesis in the tax-onomies,

• Verification, which investigates the rational agent's knowledge throughthe results of the three previous processes.

The rational agent's knowledge is voiced in a language, interpretedthrough a mental scheme, composed of objects and concepts. These objectsand concepts are organized in taxonomies, hypotheses and probes.

A rational agent interprets its knowledge which is voiced in a language. Ihave used a frame-based language Y* [11, 10, 9] to implement my prototype.

To interpret its knowledge, a rational agent has:

• A set of allowable credences C,

• A function of belief A : L x L -> C which voices the link betweentwo statements of the language. (The first will voice an object andthe second a concept. For example, the function of belief is used toascertain whether the rational agent can believe that an object verifiesa concept).

So. a mental scheme is a triplet (L, A, C) and is used to interpret statementsof the language. In our implementation C is compounded of true andunknown.

Objects and concepts are components of knowledge. They are the twopossible projections of A, the functions of belief.

/ : 6 -» C / 3e E I,, Vz E 6, A(e, z) = 7(z)

/' : 6 -+ C / 3e G Z,, Vz E O, A(z, e) = /'(z)

Our definition of object is not usual. An example of objects and concepts isgiven in figure 5.

Objects and concepts are organized in two taxonomies determined bythe generalization relationship 7. To maintain the taxonomies we needsubsumption processes [2] (i.e. To find the objects or concepts which are moreor less general than others). Hypotheses and probes organize semanticallythe objects and concepts. A hypothesis is a particular statement. A probeis a hypothesis approved by a master (see [24]). In my implementation amaster is a human expert.



(037* (zsa (W? e oz?/#en))(2- ?/ (oa/ e 502660)) This figure presents a fra-(n%2m6er (Wae 8)) me. It expresses an object(%'s component o/ (ua/ e 77137)) 37« and the concepts that(fm&ecWom (fa/?ie 037,,)) ( verifies.(is linked by (value l g)))

These statements are interpreted with the A function:A(a37g,( / ,oa;?/ en)) = fr%e, A(a37@, m6en W e. 8) =

A(a37g, (25 component o/,

The first argument of the A function is the statement of an object and thesecond is the statement of a concept. The object (2373 is a function of belieflav . It has one argument: the statement of a concept (e.g. /((z's a,value, oxygen)) = true). The concept oxygen is a function of belief too

I'oxygen- ^ has one argument: the statement of an object (e.g. I'oxygen( 7s}= vrai).

Figure 5: An example of frame

THE FORMAL FRAMEWORK

As previously mentioned, the analogical research group's model must becompleted by the rational agent's one. The correspondences between ourgroup's model and the rational agent's one will be specified. Figure 6presents the sequence of processes which are the components of analogi-

cal reasoning.Dependency relationship searching can be achieved by learning. When

the bases are given (i.e. by the search similarity process), a dependency canbe learnt. The following conjecture is made: "The rational agent is ableto learn the dependency". The bases constitute the sample (i.e. here theset of examples) of the conjecture. Learning is composed of abduction, in-duction and deduction. Abduction finds the regularities. Induction makesthe hypothesis that the solution of the problem depends on the regulari-ties. Deduction locates the hypothesis in the taxonomies and gives sets ofexamples and counter-examples. An example of a dependency relationshipsearch by learning is given in the figure 7.

Similarities searching involves setting up the mapping relationship andidentifying potential bases. For a rational agent, an object knows all theconcepts that it verifies and a concept knows all the objects which verifyit. The dependency used expresses the relevant data to solve the problem.We only consider the relevant concepts of the dependency in matching. Weknow the concepts of the target and those of the dependency. The relevantconcepts are the conjunction of these two sets. Thus a set of candidatebases can easily be determined: these are objects which verify at least one



Probe

Target

Conjecture

4| Abduction |

IRegularities

II Induction |

4Hypothesis

-^ j| Deduction I

\Example &

Counter-exampleJ > —

Similarity search

Probe &Target

*Basis

II Verification |

iBases

ITransferrall

ITarget

Processes are framed, knowledgeputs/outputs of the processes

This figure presents the processes usedfor analogical reasoning. The depen-dency relationship searching process isconstituted by three processes (i.e. ab-duction, induction, deduction). Thesample can be determined by searchingsimilar objects according to the tar-get. The conjecture is abducted andinduced to create a hypothesis. Thisis considered as a dependency. It canbe provided by the expert (i.e. a mas-ter). The given dependency is then aprobe. The dependency is located inthe taxonomy of the generalization re-lationship by deduction. The resultsare the determination of the examplesand counter-examples of the hypothe-sis or probe. The user can provide thetarget and eventually the dependency.Afterwards, the bases are given by thesimilarity search process. The basesare ordered from the most similar tothe least. The user checks the bases bysurveying the similarities and dissimi-larities of the bases to the target. If thecheck is non-verified then the rationalagent modifies or replaces the depen-dency. A new learning or deduction isthen necessary. The best one is usedfor transferring knowledge to the tar-get.

units not. The arrows point to the in-

Figure 6: The processes of analogical reasoning



/SUAUSA TION \ option* fichi«r m@l#ewl*

VISUALISATION \ option* fichi«r noimcul*

Shown here are four molecules, which are synthetized by a class of reaction.Each of these molecules contains a bond (in bold-facing mode in the figure)which has been created by the reaction. We want to learn on what data

the creation of the bond depends.

(// (is a (value conjecture)}(examples (value l k\ /uu 'i44i)))

To do this, the conjecture is made: "That dependency can be learned", andwe join to this a set of examples (i.e. The four bonds in bold-facing mode

in the molecules).

Abduction determines the sub-graph (on the left) fre-quently seen in examples. Induction makes a hypothesisthat implies that the creation of the bond (in bold-facingmode) depends on the attendance of the sub-graph.

Deduction searches for the bonds which verify the hypothesis. In this case,an example of the conjecture is not an example of the hypothesis (i.e. thebond in the molecule ra^i), since it does not contain the whole sub-graph(i.e. a bond between a carbon and an oxygen atom).

Figure 7: Dependency relationship search achieved by a learning process

H



Q" "OH../....-...H

o...'. ,;• OThis figure presentssome bases similar tothe target according tothe learnt dependency.

The bases are on the leftand the target is on theright. Solid lines showpossible matching.

•o-

O

O' "H

Figure 8: An example of similarity searching

relevant concept. To identify the potential bases, only the objects whichsatisfy matching criteria and are not too dissimilar from the target areretained. The result of this process is a set of bases ordered from the mostsimilar to the least. Figure 8 presents an example of similarity searching.

Evaluating the inference is equivalent to the rational agent's verificationprocess. To verify, the user has the bases sorted from the most similar tothe least. Each one produces its similarity and dissimilarity from the targetaccording to the dependency. The user evaluates whether the similarityand dissimilarity are valid or not. As bases are determined according todependency, the invalid similarity and dissimilarity entail changes in thedependency:

• If a similarity is not valid then it is not relevant and the equivalentconcept must be removed from the dependency.

* If a dissimilarity is invalid then it is relevant and the equivalent con-cept must be added to the dependency.



Similarities :

is a — bond

is a — hypothesismu

extremity hypothesise^

extremity ~* hypothesis-im

extremity — a^g

Dissimilarities :

extremity = a^^

If we are looking for simi-lar bonds to the one in bold-facing mode according to thelearned dependency relation-ship, then the best one is in-dicated by an arrow in thefigure (i.e. J. The expertverifies the inference by con-sidering the similarities andthe dissimilarities. The bond/37m is the best as it veri-fies the sub-graph and is inthe same molecule as the tar-get (extremity = 0379). Anexpert can consider the lastlikeness as invalid. So. therational agent must modifythe used dependency. Mod-ification entails new deduc-tion or learning.

In this figure, the = symbol-izes a value facet and the a type facet.

Figure 9: Analogical inference verification

An example of verification is given in figure 9.The common knowledge transfer is a classification of the target UQ iden-

tical with the best basis ty one. According to the problem, other specificknowledge transfers are added. These knowledge transfer functions are de-

termined by dependency.The sequence of processes is presented in figure 6. It is a cycle.

CONCLUSION

This is the first implementation of a rational agent in an object-orientedlanguage. This implementation highlights some drawbacks and differenceswith the rational agent's original model:

• The composition of the set of allowable credences and the grammarof the language adversely influence the treatment of processes.

• The modification of the taxonomies is not modelized in the original

model.



• The review and the verification should be specified.

Two of the most important notions in this framework are:

• to have a taxonomy of dependencies which allows a semantic index(i.e. the solved problems as well as the problem to be solved aremore specific than the possible dependencies),

• to have dependencies integrated in the form of object and conceptshapes.

These two characteristics are useful for improving the response time of theprocesses.

Our framework is validated by the quality of the experimental results ofthe rational-agent implementation. The used range (i.e. the synthesis in or-ganic chemistry) is complex. The following hypothesis: "The good acquiredresults in a real range validate our framework" is made. However, storagecapacity of knowledge, combinatorial of algorithms (especially matching),and quality of the interface (very important to check the reasoning) of theimplementation must be improved testing.

ACKNOWLEDGMENTS

This work is part of the "Groupement De Recherche : Traitement Infor-matique de la Connaissance en Chimie Organique" (Research Group: In-formation Processing of Organic-chemistry Knowledge) and was the objectof a thesis [23] financed by FRAMENTEC-COGNITECH. I should like tothank Mr Frangois Arlabosse (FRAMENTEC-COGNITECH), all who par-ticipated in GDR TICCO, and especially Mr Claude Laurengo, Mr JoelQuinqueton and my Thesis director Jean Sallantin.

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abstract introduction€¦ · synthesis in organic chemistry is difficult. it consists of creating...

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