A Tool for Advanced Correspondence Checking in Answer-Set Programming

In previous work, a general framework for specifying correspondences between logic programs under the answer-set semantics has been defined. The framework allows to define different notions of equivalence, including well-known notions like strong equivalence as well as refined ones based on the projection of answer sets, where not all parts of an answer set are of relevance (like, e.g., removal of auxiliary letters). In the general case, deciding the correspondence of two programs lies on the fourth level of the polynomial hierarchy and therefore this task can (presumably) not be efficiently reduced to answer-set programming. In this paper, we describe an implementation to verify program correspondences in this general framework. The system, called cc , relies on linear-time constructible reductions to quantified propositional logic using extant solvers for the latter language as back-end inference engines. We provide some preliminary performance evaluation which shed light on some crucial design issues. Introduction Nonmonotonic logic programs under the answer-set semantics (Gelfond & Lifschitz 1991), with which we are dealing with in this paper, represent the canonical and, due to the availability of efficient answer-set solvers, arguably most widely used approach to answer-set programming (ASP). The latter paradigm is based on the idea that problems are encoded in terms of theories such that the solutions of a given problem are determined by the models (“answer sets”) of the corresponding theory. Logic programming under the answer-set semantics has become an important host for solving many AI problems, including planning, diagnosis, and inheritance reasoning (cf. Gelfond & Leone (2002) for an overview). To support engineering tasks of ASP solutions, an important issue is to determine the equivalence of different problem encodings. To this end, various notions of equivalence between programs under the answer-set semantics This work was partially supported by the Austrian Science Fund (FWF) under grant P18019; the second author was also supported by the Austrian Federal Ministry of Transport, Innovation, and Technology (BMVIT) and the Austrian Research Promotion Agency (FFG) under grant FIT-IT-810806. have been studied in the literature, including the recently proposed framework by Eiter, Tompits, & Woltran (2005), which subsumes most of the previously introduced notions. Within this framework, correspondence between two programs, and , holds iff the answer sets of and satisfy certain criteria, for any program in a specified class, called the context. We shall focus here on correspondence problems where both the context and the comparison between answer sets are determined in terms of alphabets. This kind of program correspondence includes, as special instances, the well-known notions of strong equivalence (Lifschitz, Pearce, & Valverde 2001), uniform equivalence (Eiter & Fink 2003), its relativised variants thereof (Woltran 2004), as well as the practicably important case of program comparison under projected answer sets. In the last setting, not a whole answer set of a program is of interest, but only its intersection on a subset of all letters; this includes, in particular, removal of auxiliary letters. For illustration, consider the following two programs which both express the selection of exactly one of the atoms , . An atom can only be selected if it can be derived together with the context: