Abstract Answer Set Solvers

Lierler, Yuliya

doi:10.1007/978-3-540-89982-2_35

Cited by 22 publications

(33 citation statements)

References 11 publications

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“…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.…”

Section: Related Workmentioning

confidence: 99%

Abstract solvers for Dung’s argumentation frameworks

Brochenin

Linsbichler

Maratea

et al. 2018

AAC

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TU Wien, Austria E-mails: linsbich@dbai.tuwien.ac.at, wallner@dbai.tuwien.ac.at, woltran@dbai.tuwien.ac.at Abstract. Abstract solvers are a quite recent method to uniformly describe algorithms in a rigorous formal way via graphs. Compared to traditional methods like pseudo-code descriptions, abstract solvers have several advantages. In particular, they provide a uniform formal representation that allows for precise comparisons of different algorithms. Recently, this new methodology has proven successful in declarative paradigms such as Propositional Satisfiability and Answer Set Programming. In this paper, we apply this machinery to Dung's abstract argumentation frameworks. We first provide descriptions of several advanced algorithms for the preferred semantics in terms of abstract solvers. We also show how it is possible to obtain new abstract solutions by "combining" concepts of existing algorithms by means of combining abstract solvers. Then, we implemented a new solving procedure based on our findings in CEGARTIX, and call it CEGARTIX+. We finally show that CEGARTIX+ is competitive and complementary in its performance to CEGARTIX on benchmarks of the first and second argumentation competition.Keywords: Abstract argumentation, abstract solvers IntroductionDung's concept of abstract argumentation [23] is nowadays a core formalism in Artificial Intelligence [4,46]. The problem of solving certain reasoning tasks on such frameworks is the centerpiece of many advanced higher-level argumentation systems. The problems to be solved can however be intractable and might even be hard for the second level of the polynomial hierarchy [24,26]. Thus, efficient and advanced algorithms have to be developed in order to deal with real-world size data within reasonable performance bounds. The argumentation community is currently facing this challenge [17] [44]. Hereby, one characterizes the possible states of computation as nodes of a graph, and the techniques (i.e., the computation steps in the algorithms) as arcs between nodes. 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). We show that abstract solvers allow for convenient algorithms design resulting in a clear and mathematically precise description. Moreover, formal properties of the algorithms (i.e. correctness) are easily specified by means of related graph properties (i.e. reachability). We then illustrate how abstract solvers allow to highlight in a more clear way similarities and differences among solvin...

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Section: Related Workmentioning

confidence: 99%

Abstract solvers for Dung’s argumentation frameworks

Brochenin

Linsbichler

Maratea

et al. 2018

AAC

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“…The graph AS Π is inspired by the graph SM Π introduced by Lierler [17] for specifying answer set solver SMODELS [23]. The graph SM Π extends AS Π by two additional transition rules (in other words, inference rules or propagators): All Rules Canceled and Backchain True.…”

Section: Review: Abstract Answer Set Solvermentioning

confidence: 99%

“…The graph SM Π extends AS Π by two additional transition rules (in other words, inference rules or propagators): All Rules Canceled and Backchain True. Lierler and Truszczynski [20] developed a similar framework to model such modern answer set solvers as CMODELS [15], SUP [17], and CLASP [14]. For the simplicity of this presentation, we settle on the AS Π formalism as a choice for depicting an answer set solver.…”

Section: Review: Abstract Answer Set Solvermentioning

confidence: 99%

Prolog and ASP Inference under One Roof

Balduccini

Lierler

Schüller

2013

Logic Programming and Nonmonotonic Reasoning

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Abstract. Answer set programming (ASP) is a declarative programming paradigm stemming from logic programming that has been successfully applied in various domains. Despite amazing advancements in ASP solving, many applications still pose a challenge that is commonly referred to as grounding bottleneck. Devising, implementing, and evaluating a method that alleviates this problem for certain application domains is the focus of this paper. The proposed method is based on combining backtracking-based search algorithms employed in answer set solvers with SLDNF resolution from PROLOG. Using PROLOG inference on non-ground portions of a given program, both grounding time and the size of the ground program can be substantially reduced.

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“…Note that part of this property has been recently established also in [35], where it is discussed that consistent leaf interpretations are supported models for smodels, thus they are not guaranteed to be answer sets.…”

Section: Theoremmentioning

confidence: 99%

“…In [35], the author presents an abstract framework for designing dll-like ASP procedures in a precise mathematical way: the work adapts to logic programs under the stable model semantics the work presented in [47] for SAT and Satisfiability Modulo Theories (SMT). 18 One of the results in the paper about the relation between cmodels and smodels algorithms leads to similar conclusions as our Theorem 2; another result gives a different characterization of part of Theorem 7. dlv and other systems are not considered in the paper.…”

Section: Related Workmentioning

confidence: 99%

On the relation among answer set solvers

Giunchiglia

Leone

Maratea

2008

Ann Math Artif Intell

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In this paper, we study the relation among Answer Set Programming (ASP) systems from a computational point of view. We consider smodels, dlv, and cmodels ASP systems based on stable model semantics, the first two being native ASP systems and the last being a SAT-based system. We first show that smodels, dlv, and cmodels explore search trees with the same branching nodes (assuming, of course, a same branching heuristic) on the class of tight logic programs. Leveraging on the fact that SAT-based systems rely on the deeply studied Davis-LogemannLoveland (dll) algorithm, we derive new complexity results for the ASP procedures. We also show that on nontight programs the SAT-based systems are computationally different from native procedures, and the latter have computational advantages. Moreover, we show that native procedures can guarantee the "correctness" of a reported solution when reaching the leaves of the search trees (i.e., no stability check is needed), while this is not the case for SAT-based procedures on nontight programs. A similar advantage holds for dlv in comparison with smodels if the "well-founded" operator is disabled and only Fitting's operator is used for negative inferences. We finally study the "cost" of achieving such advantages and comment on to what extent the results presented extend to other systems.A preliminary version of a part of the results presented in this work has been published in [25].

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Abstract Answer Set Solvers

Cited by 22 publications

References 11 publications

Abstract solvers for Dung’s argumentation frameworks

Abstract solvers for Dung’s argumentation frameworks

Prolog and ASP Inference under One Roof

On the relation among answer set solvers

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