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14
Pattern Structures and Their Projections
, 2001
"... Pattern structures consist of objects with descriptions (called patterns) that allow a semilattice operation on them. Pattern structures arise naturally from ordered data, e.g., from labeled graphs ordered by graph morphisms. It is shown that pattern structures can be reduced to formal contexts, ..."
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Cited by 39 (11 self)
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Pattern structures consist of objects with descriptions (called patterns) that allow a semilattice operation on them. Pattern structures arise naturally from ordered data, e.g., from labeled graphs ordered by graph morphisms. It is shown that pattern structures can be reduced to formal contexts, however sometimes processing the former is often more ecient and obvious than processing the latter. Concepts, implications, plausible hypotheses, and classi cations are de ned for data given by pattern structures. Since computation in pattern structures may be intractable, approximations of patterns by means of projections are introduced.
Nested Graphs: A Graphbased Knowledge Representation Model with FOL Semantics
 Proceedings of the 6th International Conference on Knowledge Representation (KR'98
, 1998
"... We present a graphbased KR model issued from Sowa's conceptual graphs but studied and developed with a speci c approach. Formal objects are kinds of labelled graphs, which maybesimple graphs or nested graphs. The fundamental notion for doing reasonings, called projection (or subsumption), is a kind ..."
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Cited by 23 (5 self)
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We present a graphbased KR model issued from Sowa's conceptual graphs but studied and developed with a speci c approach. Formal objects are kinds of labelled graphs, which maybesimple graphs or nested graphs. The fundamental notion for doing reasonings, called projection (or subsumption), is a kind of labelled graph morphism. Thus, we propose a graphical KR model, where \graphical " is used in the sense of [Sch91], i.e. a model that \uses graphtheoretic notions in an essential and nontrivial way". Indeed, morphism, which is the fundamental notion for any structure, is at the core of our theory. We de ne two rst order logic semantics, which correspond to di erentintuitivesemantics, and proveinboth cases that projection is sound and complete with respect to deduction. This paper is almost identical to the paper appeared in the KR'98 proceedings. It provides minor corrections. 1
Sound and Complete Forward and Backward Chainings of Graph Rules
, 1996
"... This paper presents graph operations for processing conceptual graph rules in forward chaining and backward chaining. In both cases the operations provide sound and complete procedures with respect to firstorder logic deduction. First we present our framework: simple conceptual graphs, rules as cou ..."
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Cited by 22 (9 self)
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This paper presents graph operations for processing conceptual graph rules in forward chaining and backward chaining. In both cases the operations provide sound and complete procedures with respect to firstorder logic deduction. First we present our framework: simple conceptual graphs, rules as couples of lambdaabstractions, knowledge base, logical semantics. Next we focus on forward chaining. In particular, using the notion of redundancy, we exactly characterize when the application of a rule to a graph enriches or not this graph with a "new" information. The forward mechanism is complete if the knowledge base is in normal form. Basic notions (cut points, pieces, compatible partitions, unification) for backward chaining are detailed. A parallel with previous works on backward chaining is done, in particular with the work of B.C. Ghosh and V. Wuwongse, which is close to ours. The main difference is that we do not split the goals into trivial subgraphs (a relation and its neighbours...
RELIEF: Combining expressiveness and rapidity into a single system
, 1998
"... This paper constitutes a proposal for an efficient and effective logical information retrieval system. Following a relational indexing approach, which is in our opinion a necessity to cope with the emerging applications such as those based on multimedia, we use the conceptual graphs formalism as our ..."
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Cited by 21 (3 self)
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This paper constitutes a proposal for an efficient and effective logical information retrieval system. Following a relational indexing approach, which is in our opinion a necessity to cope with the emerging applications such as those based on multimedia, we use the conceptual graphs formalism as our indexing language. This choice allows for relational indexing support and captures all the useful properties of the logical information retrieval model, in a workable system. First order logic and standard information retrieval techniques are combined together, to the same effect: obtaining an expressive system, able to accurately handle complex documents, improve retrieval effectiveness, and achieve good time performance. Experimentations on an image test collection, within a system available on the Web, provide an illustration of the role that logic may have in the future development of information retrieval systems. 1 Introduction The emergence of new applications, such as those based ...
Extensions of Simple Conceptual Graphs: the Complexity of Rules and Constraints
 JOUR. OF ARTIF. INTELL. RES
, 2002
"... Simple conceptual graphs are considered as the kernel of most knowledge representation formalisms built upon $owa's model. Reasoning in this model can be expressed by a graph homomorphism called projection, whose semantics is usually given in terms of positive, conjunctive, existential FOL. We pr ..."
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Cited by 19 (1 self)
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Simple conceptual graphs are considered as the kernel of most knowledge representation formalisms built upon $owa's model. Reasoning in this model can be expressed by a graph homomorphism called projection, whose semantics is usually given in terms of positive, conjunctive, existential FOL. We present here a family of extensions of this model, based on rules and constraints, keeping graph homomorphism as the basic operation. We focus on the formal definitions of the different models obtained, including their operational semantics and relationships with FOL, and we analyze the decidability and complexity of the associated problems (consistency and deduction). As soon as rules are involved in reasonings, these problems are not decidable, but we exhibit a condition under which they fall in the polynomial hierarchy. These results extend and complete the ones already published by the authors. Moreover we systematically study the complexity of some particular cases obtained by restricting the form of constraints and/or rules.
Positive Nested Conceptual Graphs
 Proc. 5th Int’l Conf. on Conceptual Structures (ICCS 97), Springer Verlag, LNAI 1257
"... . This paper deals with positive (i.e. without negation) nested conceptual graphs (NCGs). We first give a general framework  graphs of graphs provided with morphism  for defining classes of NCGs. Then we define a new class of NCGs  typed NCGs  and we show that known kinds of NCGs can be desc ..."
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Cited by 16 (2 self)
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. This paper deals with positive (i.e. without negation) nested conceptual graphs (NCGs). We first give a general framework  graphs of graphs provided with morphism  for defining classes of NCGs. Then we define a new class of NCGs  typed NCGs  and we show that known kinds of NCGs can be described very simply as classes of the general framework. All NCG models considered generalize the simple CG model in the sense that they involve objects which are generalizations of simple CGs and reasonings on these objects are based on a graph operation (projection) which is a generalization of that used for simple CGs. Furthermore, the general framework introduced allows one to consider all these models as slight variations of a unique notion. This study has been initiated by applications we are currently involved in. 1. Introduction The work reported in this paper concerns conceptual graphs (CGs) for representing and reasoning on hierarchically structured knowledge. In these CGs, ...
Knowledge Representation and Reasonings Based on Graph Homomorphism
 In Proc. ICCS’00, volume 1867 of LNAI
, 2000
"... The main conceptual contribution in this paper is to present an approach to knowledge representation and reasonings based on labeled graphs and labeled graph homomorphism. Strengths and weaknesses of this graphbased approach are discussed. Main technical contributions are the followings. Fundam ..."
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Cited by 12 (3 self)
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The main conceptual contribution in this paper is to present an approach to knowledge representation and reasonings based on labeled graphs and labeled graph homomorphism. Strengths and weaknesses of this graphbased approach are discussed. Main technical contributions are the followings. Fundamental results about the kernel of this approach, the socalled simple graphs model are synthesized. It is then shown that the basic deduction problem on simple graphs is essentially the same problem as conjunctive query containment in databases and constraint satisfaction; polynomial parsimonious transformations between these problems are exhibited. Grounded on the simple graphs model, a knowledge representation and reasoning model allowing to deal with facts, production rules, transformation rules, and constraints is presented, as an illustration of the graphbased approach. Introduction The main conceptual contribution in this paper is to present an approach to knowledge represen...
Conceptual Graphs are also Graphs
 LIRMM (CNRS & Universite de Montpellier II), 161, rue Ada, 34392 Montpellier Cedex 5
, 1995
"... . The main objective of this paper is to add one more brick in building the CG model as a knowledge representation model autonomous from logic. The CG model is not only a graphical representation of logic, it is much more: it is a declarative model encoding knowledge in a mathematical theory, na ..."
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Cited by 11 (3 self)
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. The main objective of this paper is to add one more brick in building the CG model as a knowledge representation model autonomous from logic. The CG model is not only a graphical representation of logic, it is much more: it is a declarative model encoding knowledge in a mathematical theory, namely labelled graph theory, which has efficient computable forms, with a fundamental graph operation on the encodings to do reasoning, projection, which is a labelled graph morphism. Main topics of this paper are: a generalized formalism for simple CGs; a strong equivalence between CSP (Constraint Satisfaction Problem) and labelled graph morphism. This correspondence allows the transportation of efficient algorithms from one domain to the other, and confirms that projection or more generally labelled graph morphism firmly moors CGs to combinatorial algorithmics, which is a cornerstone of computer science. The usual sound and complete first order logic semantics for CGs is stil...
Simple Concept Graphs: A Logic Approach
 Chein (Eds.): Conceptual Structures: Theory, Tools and Applications. LNAI 1453
, 1998
"... Conceptual Graphs and Formal Concept Analysis are combined by developing a logical theory for concept graphs of relational contexts. Therefore, concept graphs are introduced as syntactical constructs, and their semantics is defined based on relational contexts. For this contextual logic, a sound and ..."
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Cited by 11 (1 self)
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Conceptual Graphs and Formal Concept Analysis are combined by developing a logical theory for concept graphs of relational contexts. Therefore, concept graphs are introduced as syntactical constructs, and their semantics is defined based on relational contexts. For this contextual logic, a sound and complete system of inference rules is presented and a standard graph is introduced that entails all concept graphs being valid in a given relational context. A possible use for conceptual knowledge representation and processing is suggested.
The CORALI Project: From Conceptual Graphs to Conceptual Graphs via Labelled Graphs
 in Proceedings of the Fifth International Conference on Conceptual Structures, ICCS'97
, 1997
"... . 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]. ..."
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Cited by 6 (0 self)
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. 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 t...