Various problems in artificial intelligence can be solved by translating them into a quantified boolean formula (QBF) and evaluating the resulting encoding. In this approach, a QBF solver is used as a black box in a rapid implementation of a more general reasoning system. Most of the current solvers for QBFs require formulas in prenex conjunctive normal form as input, which makes a further translation necessary, since the encodings are usually not in a specific normal form. This additional step increases the number of variables in the formula or disrupts the formula’s structure. Moreover, the most important part of this transformation, prenexing, is not deterministic. In this paper, we focus on an alternative way to process QBFs without these drawbacks and describe a solver, qpro, which is able to handle arbitrary formulas. To this end, we extend algorithms for QBFs to the non-normal form case and compare qpro with the leading normal form provers on several problems from the area of artificial intelligence. We prove properties of the algorithms generalized to non-clausal form by using a novel approach based on a sequent-style formulation of the calculus. 1.

Abstract. In recent work, a general framework for specifying program correspondences under the answer-set semantics has been defined. The framework allows to define different notions of equivalence, including the well-known notions of strong and uniform equivalence, as well as refined equivalence notions 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 give an overview about an implementation to compute program correspondences in this general framework. The system, called eqcheck, 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. 1

Equilibrium logic is an approach to nonmonotonic reasoning that extends the stable model and answer-set semantics for logic programs. In particular, it includes the general case of nested logic programs, where arbitrary Boolean combinations are permitted in heads and bodies of rules, as special kinds of theories. In this paper, we present efficient reductions of the main reasoning tasks associated with equilibrium logic and nested logic programs into quantified propositional logic, an extension of classical propositional logic where quantifications over atomic formulas are permitted. Thus, quantified propositional logic is a fragment of second-order logic, and its formulas are usually referred to as quantified Boolean formulas (QBFs). We provide reductions not only for decision problems, but also for the central semantical objects of equilibrium logic and nested logic programs. In particular, our encodings map a given reasoning task into some QBF such that the latter is valid precisely in case the former holds. The reasoning tasks we deal with here are the consistency problem, brave reasoning, and skeptical reasoning. Additionally, we also provide encodings for testing equivalence of theories or programs under different notions of equivalence, viz. ordinary, strong, and uniform equivalence. For all considered reasoning tasks, we analyse their computational complexity and give strict complexity bounds. Hereby, our encodings yield upper

Abstract. In recent work, a general framework for specifying correspondences between logic programs under the answer-set semantics has been defined. The framework captures different notions of equivalence, including well-known ones like ordinary, strong, and uniform equivalence, as well as refined ones based on the projection of answer sets where not all parts of an answer set are of relevance. 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 and uses extant solvers for the latter language as back-end inference engines. 1 General Information To support engineering tasks in answer-set programming (ASP) [4], an important issue is to determine the equivalence of different problem encodings, given by two logic programs. Various notions of equivalence between programs have been studied in the literature [7, 2, 11] including the recently proposed framework by Eiter et al. [3], which subsumes most of the previously introduced notions. Within this framework, correspondence

Abstract. The tool cc ⊤ is an implementation for testing various parameterised notions of program correspondence between logic programs under the answerset semantics, based on reductions to quantified propositional logic. One such notion is relativised uniform equivalence with projection, which extends standard uniform equivalence via two additional parameters: one for specifying the input alphabet and one for specifying the output alphabet. In particular, the latter parameter is used for projecting answer sets to the set of designated output atoms, i.e., ignoring auxiliary atoms during answer-set comparison. In this paper, we discuss an application of cc ⊤ for verifying the correctness of students ’ solutions drawn from a laboratory course on logic programming, employing relativised uniform equivalence with projection as the underlying program correspondence notion. We complement our investigation by discussing a performance evaluation of cc⊤, showing that discriminating among different back-end solvers for quantified propositional logic is a crucial issue towards optimal performance. 1