Transition systems for model generators—A unifying approach

Lierler, Yuliya; Truszczyński, Mirosław

doi:10.1017/s1471068411000214

Cited by 19 publications

(27 citation statements)

References 23 publications

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“…Input stable models have an elegant direct characterization in terms of stable models that extends the corresponding characterization for the finitary case given by Lierler and Truszczynski [13]. Let Π be a program.…”

Section: Programsmentioning

confidence: 84%

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Connecting First-Order ASP and the Logic FO(ID) through Reducts

Truszczyński

2012

Correct Reasoning

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Abstract. Recently, an answer-set programming (ASP) formalism of logic programing with the answer-set semantics has been extended to the full first-order setting. Earlier an extension of first-order logic with inductive definitions, the logic FO(ID), was proposed as a knowledge representation formalism and developed as an alternative ASP language. We present characterizations of these formalisms in terms of concepts of infinitary propositional logic. We use them to find a direct connection between the first-order ASP and the logic FO(ID) under some restrictions on the form of theories (programs) considered.

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Section: Programsmentioning

confidence: 84%

“…We denote by A The concept of an input stable model was introduced and studied by Lierler and Truszczynski [13] as the basis for the formalism SM(ASP). It is closely related to models of modular logic programming systems [12,17,3].…”

Section: Programsmentioning

confidence: 99%

Connecting First-Order ASP and the Logic FO(ID) through Reducts

Truszczyński

2012

Correct Reasoning

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“…systems able to deal with a combination of ASP and constraint programming, a language useful to represent and reason on hybrid domains, has been put forward in [37]. Other works on abstract solvers are [38], where solvers for different formalisms, e.g. ASP and SAT with Inductive Definitions, are compared by means of comparison of the related graphs, and the following series of papers where, starting from a developed concept of modularity in answer set solving [39], abstract modeling of solvers for multi-logic systems are presented [40][41][42].…”

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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“…We start by introducing a concept in spirit of an input answer set by Lierler and Truszczynski (2011). 1 In particular, we consider input answer sets "relative to input vocabularies".…”

Section: Constraint Answer Set Programsmentioning

confidence: 99%

On relation between constraint answer set programming and satisfiability modulo theories

Lierler¹,

Susman²

2017

Theory and Practice of Logic Programming

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Constraint answer set programming is a promising research direction that integrates answer set programming with constraint processing. It is often informally related to the field of satisfiability modulo theories. Yet, the exact formal link is obscured as the terminology and concepts used in these two research areas differ. In this paper, we connect these two research areas by uncovering the precise formal relation between them. We believe that this work will booster the cross-fertilization of the theoretical foundations and the existing solving methods in both areas. As a step in this direction we provide a translation from constraint answer set programs with integer linear constraints to satisfiability modulo linear integer arithmetic that paves the way to utilizing modern satisfiability modulo theories solvers for computing answer sets of constraint answer set programs. Under consideration in Theory and Practice of Logic Programming (TPLP).

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Transition systems for model generators—A unifying approach

Cited by 19 publications

References 23 publications

Connecting First-Order ASP and the Logic FO(ID) through Reducts

Connecting First-Order ASP and the Logic FO(ID) through Reducts

Abstract solvers for Dung’s argumentation frameworks

On relation between constraint answer set programming and satisfiability modulo theories

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