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18
The stories of logic and information
 In Handbook of the Philosophy of Information, P. Adriaans and
, 2008
"... ..."
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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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.
Some algorithmic improvements for the containment problem of conjunctive queries with negation
 In ICDT
, 2007
"... Abstract. Query containment is a fundamental problem of databases. Given two queries q1 and q2, it asks whether the set of answers to q1 is included in the set of answers to q2 for any database. In this paper, we investigate this problem for conjunctive queries with negated subgoals. We use graph ho ..."
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Cited by 4 (2 self)
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Abstract. Query containment is a fundamental problem of databases. Given two queries q1 and q2, it asks whether the set of answers to q1 is included in the set of answers to q2 for any database. In this paper, we investigate this problem for conjunctive queries with negated subgoals. We use graph homomorphism as the core notion, which leads us to extend the results presented in [Ull97] and [WL03]. First, we exhibit sufficient (but not necessary) conditions for query containment based on special subgraphs of q2, which generalize that proposed in [WL03]. As a corollary, we obtain a case where the time complexity of the problem decreases. From a practical viewpoint, these properties can be exploited in algorithms, as shown in the paper. Second, we propose an algorithm based on the exploration of a space of graphs, which improves existing algorithms. 1
Default conceptual graph rules, atomic negation and TicTacToe
 in "ICCS’10: 18th International Conference on Conceptual Structures  Conceptual Structures: From Information to Intelligence", Malaisie
"... Abstract. In this paper, we explore the expressivity of default CG rules (a CGoriented subset of Reiter’s default logics) through two applications. In the first one, we show that default CG rules provide a unifying framework for CG rules as well as polarized CGs (CGs with atomic negation). This fra ..."
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Abstract. In this paper, we explore the expressivity of default CG rules (a CGoriented subset of Reiter’s default logics) through two applications. In the first one, we show that default CG rules provide a unifying framework for CG rules as well as polarized CGs (CGs with atomic negation). This framework allows us to study decidable subclasses of a new language mixing CG rules with atomic negation. In the second application, we use default CG rules as a formalism to model a game, an application seldom explored by the CG community. This model puts into light the conciseness provided by defaults, as well as the possibilities they offer to achieve efficient reasonings. 1
The Categorial FineStructure of Natural Language
, 2003
"... Categorial grammar analyzes linguistic syntax and semantics in terms of type theory and lambda calculus. A major attraction of this approach is its unifying power, as its basic function/argument structures occur across the foundations of mathematics, language and computation. This paper considers, i ..."
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Cited by 3 (1 self)
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Categorial grammar analyzes linguistic syntax and semantics in terms of type theory and lambda calculus. A major attraction of this approach is its unifying power, as its basic function/argument structures occur across the foundations of mathematics, language and computation. This paper considers, in a light examplebased manner, where this elegant logical paradigm stands when confronted with the wear and tear of reality. Starting from a brief history of the Lambek tradition since the 1980s, we discuss three main issues: (a) the fit of the lambda calculus engine to characteristic semantic structures in natural language, (b) the coexistence of the original typetheoretic and more recent modal interpretations of categorial logics, and (c) the place of categorial grammars in the complex total architecture of natural language, which involves  amongst others  mixtures of interpretation and inference.
Complexity Boundaries for Generalized Guarded Existential Rules
, 2011
"... In this report, we establish complexities of the conjunctive query entailment problem for classes of existential rules (also called TupleGenerating Dependencies or Datalog+/ rules). Our contribution is twofold. First, we introduce the class of greedy bounded treewidth sets (gbts) of rules, which ..."
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In this report, we establish complexities of the conjunctive query entailment problem for classes of existential rules (also called TupleGenerating Dependencies or Datalog+/ rules). Our contribution is twofold. First, we introduce the class of greedy bounded treewidth sets (gbts) of rules, which covers guarded rules, and their known generalizations, namely (weakly) frontierguarded rules. We provide a generic algorithm for query entailment with gbts, which is worstcase optimal for combined complexity with bounded predicate arity, as well as for data complexity. Secondly, we classify several gbts classes, whose complexity was unknown, namely frontierone, frontierguarded and weakly frontierguarded rules, with respect to combined complexity (with both unbounded and bounded predicate arity) and data complexity. 1
Simple conceptual graphs and simple concept graphs
 In Øhrstrøm et al
"... Abstract. Sowa’s Conceptual Graphs and Formal Concept Analysis have been combined into another knowledge representation formalism named Concept Graphs. In this paper, we compare Simple Conceptual Graphs with Simple Concept Graphs, by successively studying their different syntaxes, semantics, and en ..."
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Abstract. Sowa’s Conceptual Graphs and Formal Concept Analysis have been combined into another knowledge representation formalism named Concept Graphs. In this paper, we compare Simple Conceptual Graphs with Simple Concept Graphs, by successively studying their different syntaxes, semantics, and entailment calculus. We show that these graphs are almost identical mathematical objects, have equivalent semantics, and similar inference mechanisms. We highlight the respective benefits of these two graphbased knowledge representation formalisms, and propose to unify them. 1
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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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
Guards, Bounds, and Generalized Semantics
, 2005
"... Some initial motivations for the Guarded Fragment still seem of interest in carrying its program further. First, we stress the equivalence between two perspectives: (a) satisfiability on standard models for guarded firstorder formulas, and (b) satisfiability on general assignment models for arbitra ..."
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Some initial motivations for the Guarded Fragment still seem of interest in carrying its program further. First, we stress the equivalence between two perspectives: (a) satisfiability on standard models for guarded firstorder formulas, and (b) satisfiability on general assignment models for arbitrary firstorder formulas. In particular, we give a new straightforward reduction from the former notion to the latter. We also show how a perspective shift to general assignment models provides a new look at the fixedpoint extension LFP(FO) of firstorder logic, making it decidable. Next, we relate guarded syntax to earlier quantifier restriction strategies for the purpose of achieving effective axiomatizability in secondorder logic  pointing at analogies with 'persistent' formulas, which are essentially in the Bounded Fragment of manysorted firstorder logic. Finally, we look at some further unexplored directions, including the systematic use of 'quasimodels' as a semantics by itself.