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Weak equivalence for constraint sets

Sieger van Denneheuvel, Karen L. Kwast

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Abstract

We describe a generalization of equivalence between constraint sets, called weak equivalence. This new equivalence relation takes into account that not all variables have the same function in a constraint set and therefore distinguishes between restriction variables and intermediate variables. We explore the properties of weak equivalence and its underlying notion of weak implication with an axiomatic approach. In addition a complete set of axioms for weak implication is presented. With examples derived from the declarative rule language RL we show the applicability of weak equivalence to constraint solving. 1

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What this paper is about

We describe a generalization of equivalence between constraint sets, called weak equivalence. This new equivalence relation takes into account that not all variables have the same function in a constraint set and therefore distinguishes between restriction variables and intermediate variables. We explore the properties of weak equivalence and its underlying notion of weak implication with an axiomatic approach. In addition a complete set of axioms for weak implication is presented. With examples derived from the declarative rule language RL we show the applicability of weak equivalence to constraint solving. 1

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Available abstract

We describe a generalization of equivalence between constraint sets, called weak equivalence. This new equivalence relation takes into account that not all variables have the same function in a constraint set and therefore distinguishes between restriction variables and intermediate variables. We explore the properties of weak equivalence and its underlying notion of weak implication with an axiomatic approach. In addition a complete set of axioms for weak implication is presented. With examples derived from the declarative rule language RL we show the applicability of weak equivalence to constraint solving. 1

Key concepts: Equivalence (formal languages), Axiom, Equivalence relation, Mathematics, Constraint (computer-aided design), Logical equivalence, Generalization, Discrete mathematics

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