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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.
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.
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
Kamp's Theorem for Intervals
"... We show the analogue of Kamp's theorem for intervals on Dedekind complete flows of time. More precisely, every first order definable set of pairs of time points is definable from ordinary LTL formulas and the binary versions of until and since using just composition and casedistinction as logical o ..."
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We show the analogue of Kamp's theorem for intervals on Dedekind complete flows of time. More precisely, every first order definable set of pairs of time points is definable from ordinary LTL formulas and the binary versions of until and since using just composition and casedistinction as logical operations. Kamp's Theorem follows as a corollary.
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.
Principal Adviser
, 2006
"... is fully adequate in scope and quality as a dissertation for the degree ..."
Categorial Grammar at a CrossRoads
, 2003
"... Categorial grammars are driven by substructural logics. These are fragments of modal logics for the structures the grammar deals with. We will discuss modal language as a means of access to families of relevant structures: formal languages, type hierarchies, relation algebrasarrow models, and vect ..."
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Categorial grammars are driven by substructural logics. These are fragments of modal logics for the structures the grammar deals with. We will discuss modal language as a means of access to families of relevant structures: formal languages, type hierarchies, relation algebrasarrow models, and vector spaces. This is the crossroads of our title, where open directions abound.