Abstract answer set solvers with backjumping and learning

Abstract

Nieuwenhuis et al. (2006. Solving SAT and SAT modulo theories: From an abstract DavisPutnam-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, smodels cc , 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.

Abstract solvers for Dung’s argumentation frameworks

“…We do so by using benchmarks of the first and second argumentation competition, as well as instances from earlier work. This is an interesting result which shows that a combination based on abstract solvers is proven to be also useful in practice (for similar observations, see [36,44]). We finally show (with focus on CEGARTIX), how reasoning tasks under further semantics, other than preferred, can be solved with this framework, and demonstrate how optimizations are easily added to our abstract solvers in a modular way.…”

“…Only few of the aforementioned works [36,44] have already aimed for the implementation of combinations of algorithms based on abstract solvers; thus, our practical results are particularly remarkable.…”

“…where the SAT calls are made to provide satisfying assignments of the Boolean abstraction of the SMT problem that are then checked for "SMT consistency". Lierler [35] imported this methodology to Answer Set Programming (ASP), by first designing abstract solvers for some backtracking-based ASP solvers for non-disjunctive ASP solving, and then enhancing her approach to include backjumping and learning techniques [36]. Another extension for describing CASP solvers, i.e.…”

“…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).…”