We present a graph-based 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 graph-theoretic 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 ap-peared in the KR'98 proceedings. It provides mi-nor corrections. 1

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.

. 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, ...

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 graph-based approach are discussed. Main technical contributions are the followings. Fundamental results about the kernel of this approach, the so-called 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 graph-based approach. Introduction The main conceptual contribution in this paper is to present an approach to knowledge represen...

. 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...

the need to provide a model and syntax extension to specify the provenance of RDF graphs.