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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 ..."
Abstract

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
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.
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...
On querying simple conceptual graphs with negation
 IN: DATA AND KNOWLEDGE ENGINEERING, DKE, ELSEVIER, REVISED VERSION OF R.R. LIRMM
, 2006
"... We consider basic conceptual graphs, namely simple conceptual graphs (SGs), which are equivalent to the existential conjunctive positive fragment of firstorder logic. The fundamental problem, deduction, is performed by a graph homomorphism called projection. The existence of a projection from a SG ..."
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Cited by 8 (3 self)
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We consider basic conceptual graphs, namely simple conceptual graphs (SGs), which are equivalent to the existential conjunctive positive fragment of firstorder logic. The fundamental problem, deduction, is performed by a graph homomorphism called projection. The existence of a projection from a SG Q to a SG G means that the knowledge represented by Q is deducible from the knowledge represented by G. In this framework, a knowledge base is composed of SGs representing facts and a query is itself a SG. We focus on the issue of querying SGs, which highlights another fundamental problem, namely query answering. Each projection from a query to a fact defines an answer to the query, with an answer being itself a SG. The query answering problem asks for all answers to a query. This paper introduces atomic negation into this framework. Several understandings of negation are explored, which are all of interest in real world applications. In particular, we focus on situations where, in the context of incomplete knowledge, classical negation is not satisfactory because deduction can be proven but there is no answer to the query. We show that intuitionistic deduction captures the notion of an answer and can be solved by projection checking. Algorithms are provided for all studied problems. They are all based on projection. They can thus be combined to deal with several kinds of negation simultaneously. Relationships with problems on conjunctive queries in databases are recalled and extended. Finally, we point out that this discussion can be put in the context of semantic web databases.
Simple Conceptual Graphs with Atomic Negation and Difference
"... Abstract. This paper studies the introduction of atomic negation into simple conceptual graphs. Several semantics of negation are explored w.r.t. the deduction problem and the query answering problem. Sound and complete algorithm schemes based on projection (or corefprojection) are provided in all ..."
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Cited by 1 (1 self)
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Abstract. This paper studies the introduction of atomic negation into simple conceptual graphs. Several semantics of negation are explored w.r.t. the deduction problem and the query answering problem. Sound and complete algorithm schemes based on projection (or corefprojection) are provided in all cases. The processing of equality/inequality is added to the framework. 1
Visual Reasoning with Graphbased Mechanisms: the Good, the Better and the Best
"... This paper presents a graphbased knowledge representation and reasoning language. This language benefits from an important syntactic operation, which is called a graph homomorphism. This operation is sound and complete with respect to logical deduction. Hence, it is possible to do logical reasoning ..."
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Cited by 1 (0 self)
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This paper presents a graphbased knowledge representation and reasoning language. This language benefits from an important syntactic operation, which is called a graph homomorphism. This operation is sound and complete with respect to logical deduction. Hence, it is possible to do logical reasoning without using the language of logic but only graphical, thus visual, notions. This paper presents the main knowledge constructs of this language, elementary graphbased reasoning mechanisms, as well as the graph homomorphism, which encompasses all these elementary transformations in one global step. We put our work in context by presenting a concrete semantic annotation application example. 1