Complete Extensions in Argumentation Coincide with 3-Valued Stable Models in Logic Programming

Wu, Yining; Caminada, Martin; Gabbay, Dov M.

doi:10.1007/s11225-009-9210-5

Cited by 62 publications

(94 citation statements)

References 18 publications

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“…The logic programming metalevel approach has been worked out in [29]. The approach is similar to the classical logic approach except that we use logic programming to represent the argumentation framework.…”

Section: The Logic Programming Metalevel Approachmentioning

confidence: 99%

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A Logical Account of Formal Argumentation

2009

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Abstract.In the current paper, we re-examine how abstract argumentation can be formulated in terms of labellings, and how the resulting theory can be applied in the field of modal logic. In particular, we are able to express the (complete) extensions of an argumentation framework as models of a set of modal logic formulas that represents the argumentation framework. Using this approach, it becomes possible to define the grounded extension in terms of modal logic entailment.

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Section: The Logic Programming Metalevel Approachmentioning

confidence: 99%

“…, y n } is the set of all arguments attacking x. We get a resulting logic program satisfying 1. each atom is the head of exactly one clause 2. the bodies of clauses consist of weakly negated atoms only For more information, we refer to [29] and [17].…”

Section: The Logic Programming Metalevel Approachmentioning

confidence: 99%

A Logical Account of Formal Argumentation

2009

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“…Among models of a program, the following models are important: partial stable models, stable models, L-stable models, regular models, and well-founded models. 2 An argumentation framework AF = (Ar, att) is transformed into the logic program P AF by identifying each argument with a ground atom as follows [30]:…”

Section: Computationmentioning

confidence: 99%

“…stable, semi-stable, grounded, preferred) labellings of AF and partial stable (resp. stable, Lstable, well-founded, regular) models of P AF [11,30]. We modify the transformation to characterize abduction in argumentation frameworks.…”

Section: Computationmentioning

confidence: 99%

Abduction in Argumentation Frameworks and Its Use in Debate Games

Sakama

2014

New Frontiers in Artificial Intelligence

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Abstract. This paper studies an abduction problem in formal argumentation frameworks. Given an argument, an agent verifies whether the argument is justified or not in its argumentation framework. If the argument is not justified, the agent seeks conditions to explain the argument in its argumentation framework. We formulate such abductive reasoning in argumentation semantics and provide its computation in logic programming. Next we apply abduction in argumentation frameworks to reasoning by players in debate games. In debate games, two players have their own argumentation frameworks and each player builds claims to refute the opponent. A player may provide false or inaccurate arguments as a tactic to win the game. We show that abduction is used not only for seeking counter-claims but also for building dishonest claims in debate games.

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“…The main contribution of this paper depends on providing a general second-order quantifier elimination result (Theorem 5.10), results for reducing circumscribed theories (Lemmas 6.4, 6.5), including annotation theories as well as results related to specific theories: Phan's argumentation theory 2 [30] (Section 6.3), a theory related to approximate reasoning (Section 6.4) and a theory formalizing a semantics of logic programs with negation, derived from considerations of [36], closely related to stable models [17,1] (Section 6.5).…”

Section: Introduction To Annotation Theories and Related Problemsmentioning

confidence: 99%

Annotation Theories over Finite Graphs

Gabbay

Szałas

2009

Stud Logica

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Abstract. In the current paper we consider theories with vocabulary containing a number of binary and unary relation symbols. Binary relation symbols represent labeled edges of a graph and unary relations represent unique annotations of the graph's nodes. Such theories, which we call annotation theories, can be used in many applications, including the formalization of argumentation, approximate reasoning, semantics of logic programs, graph coloring, etc. We address a number of problems related to annotation theories over finite models, including satisfiability, querying problem, specification of preferred models and model checking problem.We show that most of considered problems are NPTime-or co-NPTime-complete. In order to reduce the complexity for particular theories, we use second-order quantifier elimination. To our best knowledge none of existing methods works in the case of annotation theories. We then provide a new second-order quantifier elimination method for stratified theories, which is successful in the considered cases. The new result subsumes many other results, including those of [2,28,21].

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Complete Extensions in Argumentation Coincide with 3-Valued Stable Models in Logic Programming

Cited by 62 publications

References 18 publications

A Logical Account of Formal Argumentation

A Logical Account of Formal Argumentation

Abduction in Argumentation Frameworks and Its Use in Debate Games

Annotation Theories over Finite Graphs

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