Constraint Answer Set Programming without Grounding

TL;DR

This paper introduces s(CASP), a goal-directed ASP extension with constraints that avoids grounding issues, enhances expressiveness, and shows improved performance over existing ASP systems.

Contribution

It presents s(CASP), a novel goal-directed ASP system with integrated constraints, generalizing s(ASP) and outperforming traditional ASP in benchmarks.

Findings

s(CASP) can handle constraints during execution and in answer sets.

s(CASP) demonstrates improved performance in benchmarks.

s(CASP) extends ASP expressiveness without grounding limitations.

Abstract

Extending ASP with constraints (CASP) enhances its expressiveness and performance. This extension is not straightforward as the grounding phase, present in most ASP systems, removes variables and the links among them, and also causes a combinatorial explosion in the size of the program. Several methods to overcome this issue have been devised: restricting the constraint domains (e.g., discrete instead of dense), or the type (or number) of models that can be returned. In this paper we propose to incorporate constraints into s(ASP), a goal-directed, top-down execution model which implements ASP while retaining logical variables both during execution and in the answer sets. The resulting model, s(CASP), can constrain variables that, as in CLP, are kept during the execution and in the answer sets. s(CASP) inherits and generalizes the execution model of s(ASP) and is parametric w.r.t. the constraint solver. We describe this novel execution model and show through several examples the enhanced expressiveness of s(CASP) w.r.t. ASP, CLP, and other CASP systems. We also report improved performance w.r.t. other very mature, highly optimized ASP systems in some benchmarks. This paper is under consideration for publication in Theory and Practice of Logic Programming (TPLP).