and complexity

Answer set programming (ASP) is a form of declarative programming oriented towards difficult search problems. As an outgrowth of research on the use of nonmonotonic reasoning in knowledge representation, it is particularly useful in knowledge-intensive applications. ASP programs consist of rules that look like Prolog rules, but the computational mechanisms used in ASP are different: they are based on the ideas that have led to the creation of fast satisfiability solvers for propositional logic.

Abstract. This paper reports on the Second Answer Set Programming Competition. The competitions in areas of Satisfiability checking, Pseudo-Boolean constraint solving and Quantified Boolean Formula evaluation have proven to be a strong driving force for a community to develop better performing systems. Following this experience, the Answer Set Programming competition series was set up in 2007, and ran as part of the International Conference on Logic Programming and Nonmonotonic Reasoning (LPNMR). This second competition, held in conjunction with LPNMR 2009, differed from the first one in two important ways. First, while the original competition was restricted to systems designed for the answer set programming language, the sequel was open to systems designed for other modeling languages, as well. Consequently, among the contestants of the second competition were a CLP(FD) team and three model generation systems for (extensions of) classical logic. Second, this latest competition covered not only satisfiability problems but also optimization ones. We present and discuss the set-up and the results of the competition. 1

Abstract. We report on recent advancements in the development of grounder Gringo for logic programs under answer set semantics. Like its relatives, DLV and Lparse, Gringo has in the meantime reached maturity and offers a rich modeling language to program developers. The attractiveness of Gringo is fostered by the fact that it significantly extends the input language of Lparse while supporting a compatible output format, recognized by many state-of-the-art ASP solvers. 1

In this paper, we present a novel approach to the evaluation of propositional answer-set programs. In particular, for programs with bounded treewidth, our algorithm is capable of (i) computing the number of answer sets in linear time and (ii) enumerating all answer sets with linear delay. Our algorithm relies on dynamic programming. Therefore, our approach significantly differs from standard ASP systems which implement techniques stemming from SAT or CSP, and thus usually do not exploit fixed parameter properties of the programs. We provide first experimental results which underline that, for programs with low treewidth, even a prototypical implementation is competitive compared to stateof-the-art systems. 1

Abstract. We introduce the first substantial approach to preprocessing in the context of answer set solving. The idea is to simplify a logic program while identifying equivalences among its relevant constituents. These equivalences are then used for building a compact representation of the program (in terms of Boolean constraints). We implemented our approach as well as a SAT-based technique to reduce Boolean constraints. This allows us to empirically analyze both preprocessing types and to demonstrate their computational impact. 1

Abstract. A recent framework of relativized hyperequivalence of programs offers a unifying generalization of strong and uniform equivalence. It seems to be especially well suited for applications in program optimization and modular programming due to its flexibility that allows us to restrict, independently of each other, the head and body alphabets in context programs. We study relativized hyperequivalence for the three semantics of logic programs given by stable, supported and supported minimal models. For each semantics, we identify four types of contexts, depending on whether the head and body alphabets are given directly or as the complement of a given set. Hyperequivalence relative to contexts where the head and body alphabets are specified directly has been studied before. In this paper, we establish the complexity of deciding relativized hyperequivalence wrt the three other types of context programs. 1

The attractiveness of Answer Set Programming (ASP) and related paradigms for declarative problem solving is considerably due to the availability of highly efficient yet easy-to-use implementations. A major driving force for the development and improvement of tools are standardized problem representations, for several reasons. First, they relieve developers from the burden of inventing their own input formats. Second, they establish interoperability between separate tools, allowing users to easily compare and exchange them without extensively converting their problem representations. Third, they facilitate the acquisition of problem descriptions from distinct sources, which is useful for benchmarking and assessment purposes. Historically, however, standards for representing logic programs, serving as inputs to ASP systems, were mainly dictated by the few available tools. In fact, there currently are two quasi standards, namely, the formats used by lparse and dlv, incompatible with each other. As a first step towards overcoming this deficiency, this work proposes an intermediate format for ground logic programs, intended for the representation of inputs to ASP solvers. The format is not designed to be a primary input language, given that ASP systems usually deploy a second component, called a grounder, to deal with the inputs provided by users. In view of this, our format is situated intermediate a grounder and a solver, guided by the example of grounder lparse and solver smodels, the latter marking the first among nowadays a variety of solvers processing the output of lparse. However, the output format of lparse has some decisive drawbacks, namely, its restrictive range and limited extensibility. We thus propose a new intermediate language, where our major design goals are flexibility in problem representation and easy extensibility to new language constructs.

This note provides background information and references to the tutorial on recent research developments in logic programming inspired by need of knowledge representation.

Abstract. Lparse programs are logic programs with weight constraints as implemented in the SMODELS system, which constitute an important class of logic programs with constraint atoms. To effectively apply lparse programs to problem solving, a clear understanding of its semantics and representation power is indispensable. In this paper, we study the semantics of lparse programs, called the lparse semantics. We show that for a large class of programs, called strongly satisfiable programs, the lparse semantics agrees with the semantics based on conditional satisfaction. However, when the two semantics disagree, a stable model admitted by the lparse semantics may be circularly justified. We then present a transformation, by which an lparse program can be transformed to a strongly satisfiable one, so that no circular models may be generated under the current implementation of SMODELS. This leads to an investigation of a methodological issue, namely the possibility of compact representation of aggregate programs by lparse programs. We present some experimental results to compare this approach with the ones where aggregates are more explicitly handled. 1