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Set Intervals in Constraint Logic Programming: Definition and implementation of a language

Abstract : Constraint satisfaction techniques have recently been introduced in logic programming to extend the application domain of logic programming languages. Existing languages, based on these techniques, consider arithmetic constraints applied to variables taking their value in domains of integers. This makes concise and natural modeling as well as an efficient resolution of certain np-complete combinatorial problems of a set-theoretic nature difficult. We propose a solution that consists of extending the notion of integer domain to that of set domain (set of sets). We specify a set domain by an interval whose lower and upper bounds are known sets, ordered by the set-inclusion. We define the formal and concrete structure of a new logic programming language based on constraints on set domains, called conjunto. Conjunto includes the symbols of usual set operations (,, /) interpreted in relational form (s s # 1 = s # 2,) and the inclusion relation (). In addition, it provides a set of constraints called graded constraints (eg Cardinality Function) that associate a set with an arithmetic term. This allows us to deal with optimization problems by applying a cost function to measurable terms, i. e. arithmetic, associated with the ensemblist terms. The resolution of the constraints in conjunto is based on constraint satisfaction techniques by reduction of intervals extended to the treatment of set constraints. Thus, the main contribution of this thesis concerns the definition of transformation rules within a generic algorithm, which infer the local consistency of the constraints of the language by reducing the set intervals. A set of operational research applications and combinatorial mathematics were developed with conjunto, illustrating the strengths of the language in terms
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Carmen Gervet. Set Intervals in Constraint Logic Programming: Definition and implementation of a language. Artificial Intelligence [cs.AI]. Université de Franche Comté Besançon, 1995. English. ⟨tel-01742415⟩

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