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On the Semantics of Disjunctive Logic Programs

Athanasios Tsouanas 1, 2
1 PLUME - Preuves et Langages
LIP - Laboratoire de l'Informatique du Parallélisme
Abstract : In this thesis, we study denotational semantics (model-theoretic and game-theoretic) of four logic programming languages: - LP which is the most restrictive one; - DLP which extends LP by allowing disjunctions; - LPN which extends LP by allowing negations; and - DLPN which allows both The three main contributions of this dissertation can be summarized as follows: (1) An abstract framework for logic programming semantics is defined and all semantic approaches that we study are placed within this framework. We define the general notion of a truth value space as an appropriate algebraic structure that satisfies a set of axioms. The booleans form the canonical example of such a space, but we need to consider much more general ones when dealing with negation-as-failure. For this we define and study an infinite family of spaces, parametrized over an ordinal number. (2) A game semantics for LP was defined in 1986 and further studied in 1998. Then in 2005 it was extended for the case of LPN programs. Here a game semantics for DLP programs is developed in full detail; we prove that it is sound and complete with respect to the standard, minimal models semantics of Minker. (3) We define a semantic operator which transforms any given abstract semantics of a non-disjunctive language to a semantics of the"corresponding" disjunctive one. We exhibit the correctness of this transformation by proving that it preserves equivalences of semantics, and we present some applications of it, obtaining new game semantics for DLPN, among others.
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Athanasios Tsouanas. On the Semantics of Disjunctive Logic Programs. Logic in Computer Science [cs.LO]. Ecole Nationale Supérieure de Lyon, 2014. English. ⟨tel-02139060⟩

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