Integrating Answer Set Reasoning with Constraint Solving Techniques

Abstract

The paper introduces a collection of knowledge representation languages, ${\mathcal V(C)}$, parametrised over a class ${\mathcal C}$ of constraints. ${\mathcal V(C)}$ is an extension of both CR-Prolog and CASP allowing the separation of a program into two parts: a regular program of CR-Prolog and a collection of denials whose bodies contain constraints from ${\mathcal C}$ with variables ranging over large domains. We study an instance ${{\mathcal AC}_0}$ from this family where ${\mathcal C}$ is a collection of constraints of the form X − Y > K. We give brief implementation details of an algorithm computing the answer sets of programs of ${{\mathcal AC}_0}$ which does not ground constraint variables and tightly couples the “classical” ASP algorithm with an algorithm checking consistency of difference constraints. We present several examples to show the methodology of representing knowledge in ${{\mathcal AC}_0}$. The work makes it possible to solve problems which could not be solved by pure ASP or constraint solvers.