Disjunctive Logic Programming (DLP) is an advanced formalism for knowledge representation and reasoning, which is very expressive in a precise mathematical sense: it allows to express every property of finite structures that is decidable in the complexity class ΣP 2 (NPNP). Thus, under widely believed assumptions, DLP is strictly more expressive than normal (disjunction-free) logic programming, whose expressiveness is limited to properties decidable in NP. Importantly, apart from enlarging the class of applications which can be encoded in the language, disjunction often allows for representing problems of lower complexity in a simpler and more natural fashion. This paper presents the DLV system, which is widely considered the state-of-the-art implementation of disjunctive logic programming, and addresses several aspects. As for problem solving, we provide a formal definition of its kernel language, function-free disjunctive logic programs (also known as disjunctive datalog), extended by weak constraints, which are a powerful tool to express optimization problems. We then illustrate the usage of DLV as a tool for knowledge representation and reasoning, describing a new declarative programming methodology which allows one to encode complex problems (up to ∆P 3-complete problems) in a declarative fashion. On the foundational side, we provide a detailed analysis of the computational complexity of the language of

We present an extension of language A-Prolog by consistency-restoring rules with preferences, give the semantics of the new language, CR-Prolog, and show how the language can be used to formalize various types of commonsense knowledge and reasoning.

In recent research on nonmonotonic logic programming, repeatedly strong equivalence of logic programs P and Q has been considered, which holds if the programs P [ R and Q [ R have the same stable models for any other program R. This property strengthens equivalence of P and Q with respect to stable models (which is the particular case for R = ;), and has an application in program optimization. In this paper, we consider the more liberal notion of uniform equivalence, in which R ranges only over the sets of facts rather than all sets of rules. This notion, which is well-known, is particularly useful for assessing whether programs P and Q are equivalent as components in a logic program which is modularly structured. We provide semantical characterizations of uniform equivalence for disjunctive logic programs and some restricted classes, and analyze the computational cost of uniform equivalence in the propositional (ground) case. Our results, which naturally extend to answer set semantics, complement the results on strong equivalence of logic programs and pave the way for optimizations in answer set solvers as a tool for input-based problem solving.

We extend Clark's de nition of a completed program and the de nition of a loop formula due to Lin and Zhao to disjunctive logic programs. Our main result, generalizing the Lin/Zhao theorem, shows that answer sets for a disjunctive program can be characterized as the models of its completion that satisfy the loop formulas. The concept of a tight program and Fages' theorem are extended to disjunctive programs as well.

Abstract. We consider the simplification of logic programs under the stablemodel semantics, with respect to the notions of strong and uniform equivalence between logic programs, respectively. Both notions have recently been considered for nonmonotonic logic programs (the latter dates back to the 1980s, though) and provide semantic foundations for optimizing programs with input. Extending previous work, we investigate syntactic and semantic rules for program transformation, based on proper notions of consequence. We furthermore provide encodings of these notions in answer-set programming, and give characterizations of programs which are semantically equivalent to positive and Horn programs, respectively. Finally, we investigate the complexity of program simplification and determining semantical equivalence, showing that the problems range between coNP and Π P 2 complexity, and we present some tractable cases. 1

The relation between answer set programming (ASP) and propositional satisfiability (SAT) is at the center of many research papers, partly because of the tremendous performance boost of SAT solvers during last years. Various translations from ASP to SAT are known but the resulting SAT formula either includes many new variables or may have an unpractical size. There are also well known results showing a one-to-one correspondence between the answer sets of a logic program and the models of its completion. Unfortunately, these results only work for specific classes of problems. In this paper we present a SAT-based decision procedure for answer set programming that (i) deals with any (non disjunctive) logic program, (ii) works on a SAT formula without additional variables, and (iii) is guaranteed to work in polynomial space. Further, our procedure can be extended to compute all the answer sets still working in polynomial space. The experimental results of a prototypical implementation show that the approach can pay off sometimes by orders of magnitude.

Answer Set Programming (ASP) emerged in the late 1990s as a new logic programming paradigm which has been successfully applied in various application domains. Also motivated by the availability of efficient solvers for propositional satisfiability (SAT), various reductions from logic programs to SAT were introduced in the past. All these reductions either are limited to a subclass of logic programs, or introduce new variables, or may produce exponentially bigger propositional formulas. In this paper, we present a SAT-based procedure, called ASP-SAT, that (i) deals with any (non disjunctive) logic program, (ii) works on a propositional formula without additional variables (except for those possibly introduced by the clause form transformation), and (iii) is guaranteed to work in polynomial space. From a theoretical perspective, we prove soundness and completeness of ASP-SAT. From a practical perspective, we have (i) implemented ASP-SAT in Cmodels, (ii) extended the basic procedures in order to incorporate the most popular SAT reasoning strategies, and (iii) conducted an extensive comparative analysis involving also other state-of-the-art answer set solvers. The experimental analysis shows that our solver is competitive with the other solvers we considered, and that the reasoning strategies that work best on “small but hard” problems are ineffective on “big but easy” problems and vice versa.

In recent research on nonmonotonic logic programming, repeatedly strong equivalence of logic programs P and Q has been considered, which holds if the programs P ∪ R and Q ∪ R have the same answer sets for any other program R. This property strengthens the equivalence of P and Q with respect to answer sets (which is the particular case for R =∅), and has its applications in program optimization, verification, and modular logic programming. In this article, we consider more liberal notions of strong equivalence, in which the actual form of R may be syntactically restricted. On the one hand, we consider uniform equivalence where R is a set of facts, rather than a set of rules. This notion, which is well-known in the area of deductive databases, is particularly useful for assessing whether programs P and Q are equivalent as components of a logic program which is modularly structured. On the other hand, we consider relativized notions of equivalence where R ranges over rules over a fixed alphabet, and thus generalize our results to relativized notions of strong and uniform equivalence. For all these notions, we consider disjunctive logic programs in the propositional (ground) case as well as some restricted classes, providing semantical characterizations and analyzing the computational complexity. Our results, which naturally extend to answer set semantics for programs with strong negation, complement the results on strong

Abstract. Open answer set programming (OASP) is an extension of answer set programming where one may ground a program with an arbitrary superset of the program’s constants. We define a fixed point logic (FPL) extension of Clark’s completion such that open answer sets correspond to models of FPL formulas and identify a syntactic subclass of programs, called (loosely) guarded programs. Whereas reasoning with general programs in OASP is undecidable, the FPL translation of (loosely) guarded programs falls in the decidable (loosely) guarded fixed point logic (µ(L)GF). Moreover, we reduce normal closed ASP to loosely guarded OASP, enabling a characterization of an answer set semantics by µLGF formulas. Finally, we relate guarded OASP to Datalog LITE, thus linking an answer set semantics to a semantics based on fixed point models of extended stratified Datalog programs. From this correspondence, we deduce 2-EXPTIME-completeness of satisfiability checking w.r.t. (loosely) guarded programs. 1

Abstract. A conflict clause represents a backtracking solver’s analysis of why a conflict occurred. This analysis can be used to further prune the search space and to direct the search heuristic. The use of such clauses has been very important in improving the efficiency of satisfiability (SAT) solvers over the past few years, especially on structured problems coming from applications. We describe how we have adapted conflict clause techniques for use in the answer set solver Smodels. We experimentally compare the resulting program to the original Smodels program. We also compare to ASSAT and Cmodels, which take a different approach to adding clauses to constrain an answer set search. 1