Cooperation of Decision Procedures for the Satisfiability Problem
Identifieur interne : 002080 ( Istex/Corpus ); précédent : 002079; suivant : 002081Cooperation of Decision Procedures for the Satisfiability Problem
Auteurs : Christophe RingeissenSource :
- Applied Logic Series [ 1386-2790 ]
Abstract
Abstract: Constraint programming is strongly based on the use of solvers which are able to check satisfiability of constraints. We show in this paper a rule-based algorithm for solving in a modular way the satisfiability problem w.r.t. a class of theories Th. The case where Th is the union of two disjoint theories Th 1 and Th 2 is known for a long time but we study here different cases where function symbols are shared by Th 1 and Th 2. The chosen approach leads to a highly non-deterministic decomposition algorithm but drastically simplifies the understanding of the combination problem. The obtained decomposition algorithm is illustrated by the combination of non-disjoint equational theories.
Url:
DOI: 10.1007/978-94-009-0349-4_6
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We show in this paper a rule-based algorithm for solving in a modular way the satisfiability problem w.r.t. a class of theories <Emphasis Type="Italic">Th</Emphasis>. The case where <Emphasis Type="Italic">Th</Emphasis> is the union of two disjoint theories <Emphasis Type="Italic">Th</Emphasis><Subscript>1</Subscript> and <Emphasis Type="Italic">Th</Emphasis><Subscript>2</Subscript> is known for a long time but we study here different cases where function symbols are shared by <Emphasis Type="Italic">Th</Emphasis><Subscript>1</Subscript> and <Emphasis Type="Italic">Th</Emphasis><Subscript>2</Subscript>. The chosen approach leads to a highly non-deterministic decomposition algorithm but drastically simplifies the understanding of the combination problem. 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