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

Abstract Answer Set Solvers with Backjumping and Learning

Nieuwenhuis et al. (2006. Solving SAT and SAT modulo theories: From an abstract Davis-Putnam-Logemann-Loveland procedure to DPLL(T). Journal of the ACM 53(6), 937977 showed how to describe enhancements of the Davis–Putnam–Logemann–Loveland algorithm using transition systems, instead of pseudocode. We design a similar framework for several algorithms that generate answer sets for logic programs: SMODELS, SMODELScc, asp-sat with Learning (CMODELS), and a newly designed and implemented algorithm sup. This approach to describe answer set solvers makes it easier to prove their correctness, to compare them, and to design new systems

A backjumping technique for disjunctive logic programming

In this work we present a backjumping technique for Disjunctive Logic Programming under the Stable Model Semantics (SDLP). It builds upon related techniques that had originally been introduced for constraint solving, which have been adapted to propositional satisfiability testing, and recently also to non-disjunctive logic programming under the stable model semantics (SLP) [1, 2]. We focus on backjumping without clause learning, providing a new theoretical framework for backjumping in SDLP, elaborating on and exploiting peculiarities of the disjunctive setting. We present a reason calculus and associated computations, which – compared to the traditional approaches – reduces the information to be stored, while fully preserving the correctness and the efficiency of the backjumping technique, handling specific aspects of disjunction in a benign way. We implemented the proposed technique in DLV, the state-of-the-art SDLP system. We have conducted several experiments on hard random and structured instances in order to assess the impact of backjumping, using DLV with and without the backjumping method described in this paper, using as a parameter to both two different heuristic functions. Ou