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Généralisation des Jeux Combinatoires et Applications aux Langages Logiques

Abstract : Game theory had, in its origins, a vocation for social and economic sciences, with disparate applications, for example in the processing of medical data. It is perceived today as a very general paradigm of concepts and techniques, whose potential still remains to be discovered in computer science. In this thesis we study a particular branch, combinatorial game theory (with two players), in order to profit from it in the very active field of formal semantics of programming languages. Within a game, we can separate the syntactic aspect, inherent in the possible outcomes of matches, from the semantic aspect, inherent in the forecasts over the winning player and, possibly, inherent in a quantification of profit, in terms of a stake, like wealth or prestige. To model the concept of profit, the selected structure of evaluation should not necessarily be the structure of booleans (win or loose), or that of natural or relative numbers. It is enough for this structure to verify some properties, rather weak, guaranteeing the existence of a semantics, even when the play gives rise to infinite matches, as in the game of bisimulation between concurrent processes, or as in the game of logic programming. In this work, we study the semantic characterization of a logical language (with or without constraints) in terms of a game with two players. The effect of such an interpretation, beyond the intuitive model whose didactic value would deserve to be examined, makes it possible to reuse Alpha-Beta, one of the most celebrated algorithms in combinatorial game theory, as a resolution engine for logical languages. The recent and spectacular results obtained by chess programs (like the defeat of the world champion Kasparov against the IBM program Deep Blue) testify to a kind of artificial intelligence acquired by these programs that might be transposed and exploited in the resolution of logical languages. The resolution of existential conjunctive goals in a first-order theory of Horn clauses provides an interesting case. Indeed, the ability of Alpha-Beta to simplify calculation or, in other words, to prune the uninteresting paths, is not closely related to a particular type of game or profit, but to a well-chosen set of algebraic properties, satisfied by the game of logical programming. The correction of Alpha-Beta is formally proven for a very wide variety of structures. In this way, the computed values could be natural numbers, as in the case of chess, or substitutions or constraints, as in the case of logical languages.
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Contributor : Jean-Vincent Loddo Connect in order to contact the contributor
Submitted on : Thursday, January 27, 2005 - 3:03:12 PM
Last modification on : Saturday, June 25, 2022 - 8:44:48 PM
Long-term archiving on: : Friday, September 14, 2012 - 10:20:38 AM


  • HAL Id : tel-00008272, version 1



Jean-Vincent Loddo. Généralisation des Jeux Combinatoires et Applications aux Langages Logiques. Modélisation et simulation. Université Paris-Diderot - Paris VII, 2002. Français. ⟨tel-00008272⟩



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