Abstract. We provide new perspectives on the semantics of logic programs with constraints. To this end we introduce several notions of computation and propose to use the results of computations as answer sets of programs with constraints. We discuss the rationale behind different classes of computations and study the relationships among them and among the corresponding concepts of answer sets. The proposed semantics generalize the answer set semantics for programs with monotone, convex and/or arbitrary constraints described in the literature.

Abstract. This paper gives a summary of the First Answer Set Programming System Competition that was held in conjunction with the Ninth International Conference on Logic Programming and Nonmonotonic Reasoning. The aims of the competition were twofold: first, to collect challenging benchmark problems, and second, to provide a platform to assess a broad variety of Answer Set Programming systems. The competition was inspired by similar events in neighboring fields, where regular benchmarking has been a major factor behind improvements in the developed systems and their ability to address practical applications.

Abstract. We study local-search satisfiability solvers for propositional logic extended with cardinality atoms, that is, expressions that provide explicit ways to model constraints on cardinalities of sets. Adding cardinality atoms to the language of propositional logic facilitates modeling search problems and often results in concise encodings. We propose two "native" local-search solvers for theories in the extended language. We also describe techniques to reduce the problem to standard propositional satisfiability and allow us to use off-the-shelf SAT solvers. We study these methods experimentally. Our general finding is that native solvers designed specifically for the extended language perform better than indirect methods relying on SAT solvers.

Abstract. In this paper we bring together the areas of combinatorics and propositional satisfiability. Many combinatorial theorems establish, often constructively, the existence of positive integer functions, without actually providing their closed algebraic form or tight lower and upper bounds. The area of Ramsey theory is especially rich in such results. Using the problem of computing van der Waerden numbers as an example, we show that these problems can be represented by parameterized propositional theories in such a way that decisions concerning their satisfiability determine the numbers (function) in question. We show that by using general-purpose complete and local-search techniques for testing propositional satisfiability, this approach becomes effective -competitive with specialized approaches. By following it, we were able to obtain several new results pertaining to the problem of computing van der Waerden numbers. We also note that due to their properties, especially their structural simplicity and computational hardness, propositional theories that arise in this research can be of use in development, testing and benchmarking of SAT solvers. IntroductionIn this paper we discuss how the areas of propositional satisfiability and combinatorics can help advance each other. On one hand, we show that recent dramatic improvements in the efficiency of SAT solvers and their extensions make it possible to obtain new results in combinatorics simply by encoding problems as propositional theories, and then computing their models (or deciding that none exist) using off-the-shelf general-purpose SAT solvers. On the other hand, we argue that combinatorics is a rich source of structured, parameterized families of hard propositional theories, and can provide useful sets of benchmarks for developing and testing new generations of SAT solvers.In our paper we focus on the problem of computing van der Waerden numbers. The celebrated van der Waerden theorem [20] asserts that for every positive integers k and l there is a positive integer m such that every partition of {1, . . . , m} into k blocks (parts) has at least one block with an arithmetic progression of length l. The problem is to find the least such number m. This number is called the van der Waerden number W (k, l). Exact values of W (k, l) are known only for five pairs (k, l). For other combinations of k and l there are some general lower and upper bounds but they are very coarse and do not give any good idea about the actual value of W (k, l). In the paper we show that SAT solvers such as POSIT [6], and SATO [21], as well as recently developed local-search solver walkaspps [13], designed to compute models for propositional theories extended by cardinality atoms [4], can improve lower bounds for van der Waerden numbers for several combinations of parameters k and l.Theories that arise in these investigations are determined by the two parameters k and l. Therefore, they show a substantial degree of structure and similarity. Moreover, as k and l grow, these theories ...

We provide new perspectives on the semantics of logic programs with constraints. To this end we introduce several notions of computation and propose to use the results of computations as answer sets of programs with constraints. We discuss the rationale behind different classes of computations and study the relationships among them and among the corresponding concepts of answer sets. The proposed semantics generalize the answer set semantics for programs with monotone, convex and/or arbitrary constraints described in the literature.