The CORALI Project: From Conceptual Graphs to ... - CiteSeerX

The CORALI Project: From Conceptual Graphs to Conceptual Graphs via Labelled Graphs Michel Chein LIRMM (CNRS & University Montpellier 2) Email: [email protected] Abstract. The scientific objectives of the "COnceptual gRAphs at LIrmm" project and the method used to reach these objectives are presented.

1 Introduction Sowa proposed the conceptual graphs model, in the data base context, in [4], and then developed it with a very large scope in his 1984 seminal book [5]. Sowa's multiple interests (e.g., linguistics, logics, computer science, artificial intelligence, philosophy) led to a multifaceted and highly diversified CG community. A look at the impressive bibliography compiled by Wermelinger clearly shows this, and therefore we will not present our views on all aspects of the CG model. This paper is simply aimed at presenting the scientific objectives of the "COnceptual gRAphs at LIrmm" project, and the method used to reach these objectives. Some of our results were presented during ICCS, others were presented elsewhere, or only published in French. I hope that this presentation of the overall picture will fill some holes. Prior to the CORALI project there was a system, called DILEM which was developed in the late 80s by Dicky, Cogis, and myself (see for instance [1]). DILEM is a reflex programming system, based on labelled trees, for representing reactive systems. It was used to construct a Therapy Adviser in Oncology (TAO ESPRIT project 1592/86). Sowa's book showed me that his way of considering labelled bipartite graphs -and not only trees- opened interesting perspectives, that differ from those usually proposed in semantic networks literature. From its very beginning in 1991, the CORALI project, based on [16], has been scientifically managed by Mugnier and myself. However, many other people have also been involved. Boksenbaum and Libourel brought their experience in database theory, Cogis with his skill in graph algorithms, Carbonneill, Guinaldo, Haemmerlé, and Leclère, who spent three years preparing their PhD theses on the CORALI project (they are now involved in different laboratories and companies). Next year, the only ones left will be Salvat who is finishing his PhD thesis and Genest who will begin his thesis. However, different ideas have come from researchers (e.g., Levinson, Ellis, Lehmann, Willems, and others) who, in the CG community, put labelled graphs and orders at the core of their work, at some time or another. Our fundamental scientific objective can be put forward by the following question : How far it is possible to go, in knowledge representation, by exclusively using labelled graphs to represent

knowledge and labelled graph operations to do reasonings? To study this question, we use the classical four-stroke experimental methodology: - build a theoretical formal model and algorithms for solving problems in this model; - construct software tools implementing this theory; - use the preceding two points to build applications useful for real problems; and - evaluate the systems built, and loop through this 4-cycle process until satisfactory results have been obtained. This approach is outlined in Figure 1. Let us begin our look at this figure with one comment. The objects used at the different levels (user interface, formal, physical) are always labelled bipartite graphs. We believe that it is an essential feature for building intelligent cooperative systems, i.e. for knowledge programming. Indeed, there must be an "isomorphism" between what is seen by the user and the formal model, to enable faithful modeling of the actual data and problems, and to correctly interpret the results and the computations. There must be an "isomorphism" between what is seen by the user and how objects and operations are implemented, in order to understand why and how results have been obtained. The most secure way to do this is to use a homogeneous model: the same kind of objects occur at each fundamental level. For similar reasons, links I, II, III, IV which represent intuitive semantics should be in correspondence.

2 The Simple Conceptual Graphs (SCG) model 2.1 Main Simplification Conceptual graphs are introduced in the first paragraph of chapter 3 [5]. In the second paragraph, entitled "Semantic Network", Sowa states: "a conceptual graph has no meaning in isolation. Only through the semantic network are its concepts and relations linked to context, language, emotion, and perception." Figure 3.5 [5], highlights the idea that a CG has a meaning only if it is embedded in a large semantic network. Otherwise, it is simply a labelled bipartite graph. A canon is the first part of such a semantic network proposed by Sowa. However, as he notes, a canon only contains "very little knowledge of the world, and more information has to be packed into other structures..." [5; p. 96]. Generally, a formal system is inductively defined by a primitive set of objects (the basis) and by a set of rules for building new objects from existing ones (the inductive step). We used this classical way to define data of the SCG model, i.e. simple conceptual graphs.

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Fig. 1 . Classical Four-Stroke Experimental Methodology

The primitive set of objects consists of a set of labelled star graphs (each star graph represents a relation with its signature). A star graph is considered as a bipartite graph, with the central vertex called a relation vertex and the leaves called concept vertices. The label of the relation vertex is the name of the star graph, and a concept vertex is labelled by an element of the set TC x{*}, where TC is the partially ordered set of concept types and * the generic marker. The arity of a star graph r is its number of edges, and edges are labelled by 1, 2, ..., arity(r). This set of star graphs can be partially ordered, in this case if r r' then arity(r) = arity(r') and for all i the label of the ith concept vertex of r is less than or equal to the label of the ith concept vertex of r'. (In some papers, Robert Levinson proposed directed hypergraphs. We think that in doing so the homogeneity between the models used at each level might be lost, since we believe that, at least at the user interface level, a labelled graph has a much wider applicable range than a hypergraph. Note also that the first notion is that of a labelled vertex, which is similar to a term occurrence in any linear formula.) Different equivalent construction rule sets have been proposed. Sowa called them specialization rules (with their inverses called generalization rules). For instance, one can consider the set: {simplification (s), relation or concept label restriction (dr or dc), external or internal join (j1 or j2)}. With concept label restriction a new set M is introduced, called the set of individual markers, and then a concept vertex is labelled by an element of the partially ordered set TCxM{*} (* is greater than all individual markers, and any two individual markers are uncomparable). That sums up the very simple (and elegant) SCG formal system. This formal system is too simplistic to represent concepts and relations between them, indeed a concept is only represented by its position in the hierarchy T C , and by star graphs in which it appears. In this case, the semantic network is so poor that we propose to simply called it a support. Furthermore, reasonings based solely on these notions might also be simplistic. Hence, the obvious first question to study is: What can be done with the SCG model? 2.2 First Results on the SCG Formal System As briefly mentioned above, a composition of elementary rules enables derivation of a new SCG from existing ones. To ensure that a derivation sequence of a SCG G solely consists of SCGs actually used to build G, we define a derivation as follows [35]. A derivation of a SCG G is a directed graph, without directed cycles, whose vertices are labelled by conceptual graphs, such that: 1. there is a unique sink labelled by G, 2. let x be any vertex with label H; then, (a) x is a source, and H is a SCG, or (b) x has one predecessor labelled K, and H = s(K) or dr(K) or dc(K) or j1(K) or (c) x has two predecessors, labelled K1 and K2, and H = j2(K1, K 2) This allows to give a specific definition of the specialization relation [5; p.97] between SCGs: G is a specialization of H iff H appears in a derivation of G. This

relation is denoted G H. It is straightforward to dualize these notions by considering generalization operations and to prove that G is a specialization of H iff H is a generalization of G. There is a problem in theorem 3.5.2 [5] because the specialization relation is not antisymmetric, it is simply a preorder relation not an order relation. We thus studied the equivalence classes of SCG in [16], and proved, for instance, that in any class there is a unique irredundant SCG, which is the SCG of the class with the minimal cardinality. Concerning the FOL semantics of SCG discussed later, note that if is a partial order then, in the FOL fragment associated to SCG, two equivalent formulas are always obtained by a one-to-one correspondance between variables (this is also the case when projection is restricted to injective projection). Studying the relation through derivations is not very simple. However, it is possible to characterize the specialization relation by a unique operation that Sowa called projection operator, and which is usually called projection. A projection is a morphism on SCG considered as labelled bipartite graphs, i.e. preserving the two classes of vertices, preserving the edge labels, and not increasing the vertex labels. In his theorem 3.5.4, Sowa proved that if G H then there is a projection from H to G, we proved the opposite in [16]. Based on these results a derivation can be replaced by a single operation. Furthermore, as for any class of mathematical objects, this operation is the fundamental notion for SCG, since it is the notion of a morphism between SCGs. With this result, the specialization relation can be called structural subsumption and the main kind of reasonings on SCGs involve subsumption computing [6]. There is an obvious analogy with descriptive logics, which blossomed from KL-ONE (see for instance [7]), and the following fundamental question can be put forward for a knowledge representation model: Is the SCG model "equivalent" to some fragment of FOL? More specifically, is it possible to identify a fragment of FOL which is a sound and complete formal semantics for the SCG formal system SCG? The function Φ introduced by Sowa is a natural candidate for such semantics since theorem 3.5.3 [5], where a set of wff Φ(S) associated with a support S is added, proved that: If G and H are two SCGs such that G is subsumed by H then Φ(G), Φ(S) -> Φ(H). The reciprocal was proven by Mugnier [32], and published in [16]. This requires Φ (S) and one additional notion. The SCGs can not have two concept vertices with the same individual marker (they are said to be in normal form). Then one gets: let Φ (S) be the set of formulas associated with a support S. Let g and h be formulas associated with two SCGs G and H in normal form. If h is a logical consequence of Φ (S) and g, then H subsumes G. Identifying a computable (the existence problem of a projection between SCGs is trivially computable) fragment of FOL (link 1 in Figure 1, and then with the model theory in FOL link 2) was the first step in the study and development of the CG model as a knowledge representation model "autonomous" from logic, i.e. a formal system having, at least for some parts, a sound and complete logical semantics. The Figure 2 details link 1 of Figure 1.

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Fig. 2. CG as Graphical Representation of Logic and Formal System with Logical Semantics The next step is to study algorithmic problems. More precisely, labelled bipartite graph morphism algorithms must be developed. First, we proved that - as for any interesting knowledge representation model - all basic algorithmic problems in the SCG model are NP-hard ([16], [17]). Secondly, bactracking algorithms for projection computing between any SCGs have been constructed, as well as polynomial algorithms for some special cases. These algorithms are the basis of most algorithms we have developed ([31], [335], and link 4 in figure 1). These first results provide a solid kernel for a CG model. Sowa's chapter 3 [5] is essential: the SCGs formal system is based on three theorems which specify and complete three of the first four theorems of chapter 3 [5] ! (The last one (theorem

3.2.6) deals with the denotation operator. Following the same approach we used it to introduce a set theoretic formal semantics [36] (link 3 in Figure 1).) Extensions for enriching the semantic network (in Sowa's meaning), and which has until now only contained a support, can be considered. From here on, we were guided by theoretical considerations and also by actual problems. Software tools were required to tackle actual problems, and then Haemmerlé ([26], [28]) developed the CoGITo workbench. 2.3 The CoGITo Workbench Different objectives led to the main choices concerning CoGITo. CoGITo is the basis on which different applications are built, it must be extendible, portable, easy to maintain, and must be implemented in a widespread environment. The object oriented programming paradigm was then chosen, and the core of CoGITo is a set of classes in the GNU freeware version of C++ under UNIX. With the choice of object oriented programming made, the classes have to be chosen. In human/machine interactions, graphical representations of graphs allow the construction of useful interfaces. In particular, convivial graph editors are easy to build (this is the important - for applications - visual language aspect of CGs). However, a graph is a mathematical object having "natural" implementations by cells and pointers, which are analogous to the represented graphs. Explanation modules may be built by combining this property with graphical representations, allowing the user to follow computations on a faithful and "readable" image of the model. For algorithmic considerations and interface purposes, the principal classes thus correspond to objects of the theoretical model (e.g., support, hierarchy of concept types, relation signatures, concept vertex, relation vertex, SCG). These classes are equiped with methods corresponding to the operations of the model: mainly specialization operations and projection. The implemented algorithms were those which were developed in our group. Based on the same ideas (at all levels, a representation of a SCG has to be provided) we proposed BCGCT, a file format whose fields correspond to "natural" objects: e.g. support, graph, concept vertex, and relation vertex. This external format is used for saving in permanent memory and exchanging knowledge bases. 2.4 First Applications The two first applications we considered were: a question/answering system and database modeling. These topics are the basis of Sowa's first paper, but we did not know it at that time. Having a SCG database F, where each SCG represents an asserted fact, the first problem is to query this base. More specifically, if Q is a query SCG, what is the subset Q(F) of F which is the set of specializations of Q? This is the classical subsumption reasoning applied to SCGs, and it can be performed with projections between SCGs. To show what novelties SCGs can bring for this classical problem, Carbonneill developed his ROCK system, considering both exact reasoning and approximate

reasonings ([13], [10]). An important idea was that the database is not changed and only the query is modified. Different relaxations of the query have been used: mainly, splitting of the query, and replacing some concept types appearing in the query by neighbors in TC. A notion of partial projection has also been introduced and implemented. Note here that it is quite simple to propose approximate reasonings on SCGs (and more generally on any graph-based model). However, logical interpretations of these kinds of approximate reasonings can be difficult to find, and logical interpretations for the approximate reasonings implemented in ROCK have not yet been studied. ROCK also processes SCG concept type definitions (see III.1). One difficulty appears because concept type levels in the query and in the database may differ. Once again, the database is not changed and the query alone is transformed by type contraction and expansion. Several conceptual models were introduced for the relational database model. Boksenbaum, Libourel, Carbonneill, and Haemmerlé, [9] encorporated Sowa's ideas and proposed specific definitions, in the CG formalism extended with built-in relations, for relational database concepts such as schemas, data, queries, and views. In particular, they show how updates and SQL queries can be transformed into graph operations and queries. They also show how this modelization can be used to complete uncomplete queries [11] [12]. Two important extensions of the simple model emerged during these investigations: first, an extension of the semantic network in order to consider both primitive and defined types. Secondly, extension of the simple graph model to nested graphs.

2.5 A Management System for SCG Sets The need for a SCG database management system soon arose. Indeed, we planned to develop applications with large CG sets for dictionary and chemical database projects. Guinaldo built such a system, which is now integrated in CoGITo [22] [23] [24] [25]. In his system, the basic operations of any database management system (i.e., adding, deleting, and modifying a SCG), which can be searched by its name and also its content, have been implemented. He thus developed an SCG isomorphism algorithm which uses an original filter. The system can also answer a SCG query by giving the closest specializations or generalizations to the query. According to Levinson, Ellis and Lehmann, management techniques are then based on classification (with subsumption) and ordered set management. An interesting combination of classification with hashing techniques is also used.

3 Extensions of the Semantic Network 3.1 Canonical Graphs and Type Definitions

Sowa showed how some constraints can be modeled by a canonical basis, which is a set of SCGs. In [34] we proposed a study of this notion. First, beginning with the notion of well-formed SCGs, we give several equivalent definitions of a canonical SCG, each corresponding to a particular viewpoint. We then show that the correspondence between projection and specialization remains true for well-formed SCGs and for canonical SCGs (we thus introduce a notion of a linear canonical derivation). Finally, we propose an algorithm for canonical SCG recognition whose complexity is polynomially related to the complexity of computing a projection between two SCGs. For instance, the problem is polynomial when the canonical basis is a tree set, and we develop an algorithm for this particular case. Michel Leclère ([15], [30] [31]) considered concept and relation type definitions as defined by Sowa. Introducing this notion in the semantic network leads to some complications, mainly: where in TC should a new defined type be inserted? how can one reason when facts and queries may contain defined types? These difficulties arise even if a defined type has only one definition, and if type definitions are considered as (mathematical) definitions, i.e. a defined type is equivalent to its definition. Type contraction - substitution of a defined type to its definition - and type expansion - a defined type is replaced by its definition - must preserve equivalence. As Sowa states [5; p. 107]: "Type contraction deletes a complete subgraph and incorporates the equivalent information in the type label of a single concept." The first problem is the fundamental problem in descriptive logics: i.e. computation of the subsumption relation between defined terms, when the subsumption relation between primitive terms is known. The second problem arises because types may occur with different descriptive levels in a query and in some SCG facts. For instance, it is possible that there is no projection from Q to G , even if G is a specialization of Q. In [31], a simple and specific framework is stated in which these problems can be solved using only projection and graph operations. Michel Leclère also gave a logical interpretation which is sound and complete for SCG formal system. The formula Φ(def(t)) associated with the type definition def(t) of t : t(x1,..., x k ) = λx 1 ..x k G, is equal to the universal closure of t(x1 ,..., x k ) Φ'(λx1..xkG), where Φ of a lamda abstraction is the usual function Φ applied to G except that it leaves free the variables x1,..., xk . Michel Leclère also proposed a methodology for building a support extended by defined types. 3.2 Rules Production rule sets is one of the oldest models for knowledge representation which has been used in many applications, and therefore we studied SCG rules [38]. A rule r: G 1 -> G2 is a couple of lambda-abstractions (λx1..xkG1, λx1...xkG2), where the xi are co-referent. A rule r : G1 -> G2, applies to a graph G if there is a projection, Π , from G 1 to G. The resulting graph, denoted by r(G), is built from G and G 2 by merging each xi of G2 with Π(xi), the image of xi of G1 by Π. If one has a support, S, a SCG set (on S), F, a SCG rule set (on S), R, then the closure of F by R is classically defined as the SCG set, R(F), which can be obtained from F by a finite number of rule applications. To provide a logical semantics to rule application and closure, a formula Φ (r) must be associated to a rule r. Φ (λx1...xk G 1 , λx1...xk G 2 ) is the

universal closure of Φ(λx1...xkG 1) -> Φ'(λx1...xkG2). It can now be proven that the forward chaining mechanism is sound and complete. More precisely, if a SCG G is in the closure of F then Φ (G) is a logical consequence of Φ (S), Φ (F ), Φ (R). Reciprocally, if F and R are in normal form, and g is a formula associated with a normal SCG G, and g is a logical consequence of Φ (S), Φ (F), Φ (R), then there is a SCG H in the closure of F which is subsumed by G. Backward chaining has also been studied, and was also found to be sound and complete. Furthermore, a backward chaining algorithm using particular graph notions was constructed. An important point to note is that formulas associated with SCG rules are not (Horn) clauses because, in a SCG rule, the variables which are exclusive to the conclusion are existentially quantified (and not universally quantified as in clauses). (Horn) clauses can be seen as a special case of our rules only if they have no functions and all variables of the conclusion appear in the hypothesis. In these conditions, this becomes a very particular case of a SCG rule, since G2 would be composed of only one relation whose neighbors all have an individual marker or a co-reference marker. Introducing and studying SCG rules from our viewpoint led to new results which should be useful in logical programming.

4 Positive Nested Graphs : An Extension of the SCG Model In this part, we no longer investigate extensions of the semantic network, but an extension of the data. We will not detail this topic since it is presented during this conference [19]. Let us just mention that nested graphs were encountered in several applications we were involved in: in the Menelas project [8], in the modeling of databases, in the GRAFIA project [2], and more recently in document retrieval (see [21] this conference), and in a knowledge acquisition problem (see [Bos & Botella] this conference). We consider several nested CG models which form knowledge representation models for reasoning on level-structured knowledge. They all generalize the SCG model since they involve objects which are generalizations of SCGs (essentially rooted trees of SCGs), and reasoning on these objects is based on a projection which generalizes SCG projection. During this study, we introduced a general categorical framework (graphs of graphs, and trees of graphs, morphisms between these objects, and equivalence classes of such objects) for representing hierarchic structures based on graphs. We think that this could be useful in other contexts, for instance for the study of equivalence problems between graph formalisms provided with subsumption relations. Two logical sound and complete semantics have been given for positive nested graphs. First, Anne Preller [37] proposes a specific logical language where occurrences of terms are explicitly differentiated (coloured formulas). She proposes a Gentzen system which is sound and complete for projection between NCGs. Geneviève Simonet [39] then proposes a FOL sound and complete semantics extending that of SCGs. Briefly said, a new argument is added to each predicate, which represents the context (i.e. the concept vertex) in which the predicate appears.

5 Conclusion In order to validate a hypothesis and methodology, it is essential to be faithful to this hypothesis and methodology. We started with conceptual graphs and maximally simplified the knowledge around these graphs, obtaining labelled bipartite graphs also called SCGs. We provided these objects with subsumption, and studied formal semantics. As the powerfulness of the formalism is interesting (e.g., basic asserted facts are richer than in the relational data model), we developed algorithms and a workbench for constructing applications, using SCGs at each level (user interface, formal, physical). In our opinion, this latter property is mandatory if one wants to develop intelligent cooperative systems (which can also be called knowledge programming systems). Any knowledge representation model and its associated reasonings require a logical semantics, nevertheless this does not imply that this model must be restricted to an intermediary language between a user and logic. In different actual problems, it was soon necessary to leave labelled graphs and return to notions closer to Sowa's initial notion of conceptual graphs. We then enriched the semantic network by defined types and rules, and provided a FOL semantics for the introduced notions and operations. Finally, once again forced by reality, we considered nested CGs. We are now studying the extension of type definitions and of rules for positive nested CGs with co-reference links, and also extension of CoGITo. A kind of negation is already present in type definitions and rules (since in these cases some variables are universally quantified), but this is not sufficient. We are also working on some forms of negation which can considered with our tools (it is possible to do interesting things without negation in facts, but allowing some negations in queries, while assuming the closed world assumption). As for the SCG and positive NCG models, our viewpoint might lead to identification of fragments of FOL computable by graph specific techniques. We will also study, for document retrieval purposes, non-exact reasonings with CGs (e.g., plausible reasonings with some maximal join operations, relaxation reasonings with partial projections, possible reasonings with weighted partial projections) without looking, at least at the first step, for logical semantics. We hope that it will possible to actually evaluate systems and ideas on two current major actual problems: acquisition and simulation of human behaviors, and document retrieval. Since they emerged, the death of semantic network models is regularly announced, by part of the AI community. We firmly believe that regardless of the tribulations, Sowa's conceptual graph model will remain of major importance, especially if the bricks are solid, and the building is carefully constructed.

Bibliography We only give few references. Works of the quoted people from the CG community can be found in the bibliography compiled by Wermelinger.

1. 2. 3. 4. 5. 6. 7. 8.

ּM. Chein, O. Cogis. A Simple Knowledge Representation Scheme with Precise Formal Properties. In Intern. Journal of Systems Research and Information Science, vol.2, 1988, p.215-229. M. Chein, J. Bouaud, J.P. Chevallet, R. Dieng, B. Levrat, G. Sabah. Graphes concceptuels. In Actes des 5¡ Journées nationales du PRC-GDR Intelligence Artificielle. Hermès, 1995, p. 179-212. ּF. Lehmann (edt). Semantic Networks in Artificial Intelligence. Pergamon, 1992. J.F. Sowa. Conceptual Graphs for a Data Base Interface. IBM Journal of Research and Development, vol. 20, 4, 1976, p. 336-357. J.F. Sowa. Conceptual Structures. Information Processing in Mind and Machine. Addison-Wesley, 1984. W.A. Woods. Understanding Subsumption and Taxinomy: A Framework for Progress. In Principles of Semantic Networks, J.F. Sowa (edt), Morgan Kaufmann, 1991, p. 45-94. W.A. Woods, J.G. Schmolze. The KL-ONE Family. In [Lehmann, 1992], p.133177. P. Zweigenbaum, B. Bachimont, J. Bouaud, J. Charlet, J.F. Boisvieux. Issues in the Structuration and Acquisition of an Ontology for medical language undrstanding. In Natural Language and Medicazl Concept Representation, C. Safran, C. Chute, J.R. Scherrer (edts), Vevey, 1994.

Bibliography of CORALI 9.

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12. 13. 14. 15. 16. 17.

C. Boksenbaum, B. Carbonneill, O. Haemmerlé, T. Libourel. Conceptual Graphs for Relational Databases. In Proceedings of the 1st International Conference on Conceptual Structures, ICCSâ93, Quebec City, Canada, August 1993, LNAI #699, Springer Verlag, p. 142-161. B. Carbonneill, O. Haemmerlé. Proceedings of the 2nd International Workshop on PEIRCE, Quebec City, Canada, August 1993, p. 29-32 B. Carbonneill, O. Haemmerlé. Standardizing and Interfacing Relational Databases using Conceptual Graphs. In Proceedings of the 2nd International Conference on Conceptual Structures, ICCSâ94, College Park MD, USA, August 94, LNAI #699, Springer Verlag, p. 311-330. B. Carbonneill, O. Haemmerlé. Conceptual Graphs for Relational Databases : Implementation and Perspectives. In Proceedings of the 3rd International Workshop on PEIRCE, College Park MD, USA, August 94, p. 54-66. B. Carbonneill. Vers un système de représentation de connaissances et de raisonnement fondé sur les graphes conceptuels . Ph. D. thesis, University Montpellier 2, 1996. B. Carbonneill, M. Chein, O. Cogis, O. Guinaldo, O. Haemmerlé, E. Salvat, M.L. Mugnier. COnceptualgRaphs At LIrmm. In Proceedings of the 1st CGTOOLS Workshop, Sydney, Australia, August 1996, p. 5-8. M. Chein, M. Leclère. A cooperative program for the construction of a concept type lattice. In Supplement Proceedings of the 2nd International Conference on Conceptual Structures , ICCS'94, Washington, August 94, p.16-30. M. Chein, M.L. Mugnier. Conceptual Graphs : Fundamental notions. Revue d'intelligence artificielle, 6, 4, 1992, 365-406. M. Chein, M.L. Mugnier. Specialization: where do the Difficulties Occur ? In "Conceptual Structures: Theory and Implementation", Lecture Notes in Artificial

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