Disjunctive Answer Set Solvers via Templates

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 $\Sigma^P_2$-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.Comment: To appear in Theory and Practice of Logic Programming (TPLP

Technical Communications of ICLP

Abstract Abstract solvers are a recently employed method to formally analyze algorithms that earns some advantages w.r.t. traditional ways such as pseudo-code-based description. Abstract solvers proved to be a useful tool for describing, comparing and composing solving techniques in various fields such as SAT, SMT, ASP, CASP. In ASP, abstract solvers have been so far employed for describing solvers for brave reasoning tasks. In this paper we apply, for the first time, this methodology to the analysis of ASP solvers for cautious reasoning tasks. We describe and compare the available approaches in the literature, which employ techniques for computing over-and under-approximations of the solution, the last including "coherence tests" for deciding the inclusion of a single atom in the solution, a technique borrowed from backbone computation of CNF formulas. Then, we show how to improve the current abstract solvers with new techniques, in order to design new solving algorithms

On Abstract Modular Inference Systems and Solvers

Integrating diverse formalisms into modular knowledge representation systems offers increased expressivity, modeling convenience, and computational benefits. We introduce the concepts of abstract inference modules and abstract modular inference systems to study general principles behind the design and analysis of model generating programs, or solvers, for integrated multi-logic systems. We show how modules and modular systems give rise to transition graphs, which are a natural and convenient representation of solvers, an idea pioneered by the SAT community. These graphs lend themselves well to extensions that capture such important solver design features as learning. In the paper, we consider two flavors of learning for modular formalisms, local and global. We illustrate our approach by showing how it applies to answer set programming, propositional logic, multi-logic systems based on these two formalisms and, more generally, to satisfiability modulo theories