Semantics of Constraint with Optimization KIM MARRIOIT Monash University and PETER J. STUCKEY University of Melbourne Logic Programs Many applications of constraint logic programming (CLP) languages require not only testing if a set of constraints is satisfiable, but also finding the optimal solution which satisfies them. Unfortunately, the standard declarative semantics for CLP languages does not consider optimization but only constraint satisfaction. Here we give a model theoretic semantics for optimization, which is a simple extension of the standard semantics, and a corresponding operational semantics, which may be efficiently implemented. Techniques]: Logic Programming Categories and Subject Descriptors: D. 1.6 [Programming F.4. 1 [Mathematical Logic and Formal Languages]: Mathematical Lo@c logic programming; G. 1.6 [Numerical Analysis]: Optimization constrained optimization General Additional Terms: Languages, Key Words Theory Constraint logic programming, semantics and Phrases: 1. INTRODUCTION One of the most promising design is the amalgamation innovations of constraint in recent programming programming and logic language program- ming [Jaffar and Lassez 1987]. Constraints provide a powerful and natural programming paradigm, in which the objects of computation are not explicitly constructed, but rather they are implicitly defined using constraints. Applications for constraint logic programming languages have been in many diverse areas. They include
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