Disjunctive answer set solvers via templates

Abstract

Answer set programming is a declarative programming paradigm oriented towards difficult combinatorial search problems. A fundamental task in answer set programming is to compute stable models, i.e., solutions of logic programs. Answer set solvers are the programs that perform this task. The problem of deciding whether a disjunctive program has a stable model is Σ P 2 -complete. The high complexity of reasoning within disjunctive logic programming is responsible for few solvers capable of dealing with such programs, namely dlv, gnt, cmodels, clasp and wasp. In this paper we show that transition systems introduced by Nieuwenhuis, Oliveras, and Tinelli to model and analyze satisfiability solvers can be adapted for disjunctive answer set solvers. Transition systems give a unifying perspective and bring clarity in the description and comparison of solvers. They can be effectively used for analyzing, comparing and proving correctness of search algorithms as well as inspiring new ideas in the design of disjunctive answer set solvers. In this light, we introduce a general template, which accounts for major techniques implemented in disjunctive solvers. We then illustrate how this general template captures solvers dlv, gnt, and cmodels. We also show how this framework provides a convenient tool for designing new solving algorithms by means of combinations of techniques employed in different solvers.

Unifying Reasoning and Core-Guided Search for Maximum Satisfiability

“…(The recent clause tableaux proof system for MaxSAT [23] does not capture core-guided transformations or MaxSAT preprocessing, either.) The recent formalization of implicit hitting set (IHS) algorithms for optimization modulo theories of [13] captures solely extensions of the IHS approach [12,32], extending the DPLL(T) [31] which has also earlier been extended to optimization modulo theories [30] and adapted for formalizing answer set solvers [11,24] (without optimization statements).…”

Abstract solvers for Dung’s argumentation frameworks

“…pseudo-code-based descriptions. In fact, common to all algorithms is a conceptual two-level architecture of computation, similar to Answer Set Programming solvers for disjunctive logic programs [6]. The lower level corresponds to a DPLL-like search subprocedure, while the higher level part takes care of the specific theory and drives the overall algorithm.…”

“…Abstract solvers for certain disjunctive answer set solvers implementing basic backtracking have been introduced by Brochenin et al [6] and are studied in a more general way in [7]. Even more recently, abstract solvers for satisfiability of Quantified Boolean Formulas [9] and cautious reasoning in ASP [10] have been presented.…”

“…In this way, the whole solving process amounts to a path in the graph. This concept proved successful for SAT [44], and also has been applied to several variants of Answer Set Programming [6,36,37].…”

“…In this way, the whole solving process amounts to a path in the graph. This concept proved successful for SAT [44], and also has been applied to several variants of Answer Set Programming [6,36,37].In this paper, we apply abstract solvers to certain problems in Dung's argumentation frameworks. In order to understand whether abstract solvers are well suited also for this domain, we consider quite advanced algorithms for solving problems that are hard for the second level of the polynomial hierarchy -the considered algorithms range from dedicated [45] to reduction-based [13,25] approaches (see [19] for a survey).…”