Algorithms for Effective Argumentation in Classical Propositional Logic: A Connection Graph Approach

Efstathiou, Vasiliki; Hunter, Anthony

doi:10.1007/978-3-540-77684-0_19

Cited by 10 publications

(11 citation statements)

References 15 publications

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“…We have developed algorithms for generating arguments [12,13], formalizations of decision problems concerning arguments and counterarguments in quantified Boolean formaulas [2], and compilation techniques with the aim of improving the viability of argumentation based on classical logic [5].…”

Section: Discussionmentioning

confidence: 99%

Argumentation Based on Classical Logic

Besnard

Hunter

2009

Argumentation in Artificial Intelligence

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Section: Discussionmentioning

confidence: 99%

Argumentation Based on Classical Logic

Besnard

Hunter

2009

Argumentation in Artificial Intelligence

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“…• An implementation (Efstathiou and Hunter 2008) for logic-based formalisations of argumentation (Besnard and Hunter 2001), which constructs arguments using connection graphs.…”

Section: Discussionmentioning

confidence: 99%

Answer-set programming encodings for argumentation frameworks

Egly¹,

Gaggl²,

Woltran³

2010

Argument & Computation

104

109

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Answer-set programming (ASP) has emerged as a declarative programming paradigm where problems are encoded as logic programs, such that the so-called answer sets of theses programs represent the solutions of the encoded problem. The efficiency of the latest ASP solvers reached a state that makes them applicable for problems of practical importance. Consequently, problems from many different areas, including diagnosis, data integration, and graph theory, have been successfully tackled via ASP. In this work, we present such ASP-encodings for problems associated to abstract argumentation frameworks (AFs) and generalisations thereof. Our encodings are formulated as fixed queries, such that the input is the only part depending on the actual AF to process. We illustrate the functioning of this approach, which is underlying a new argumentation system called ASPARTIX in detail and show its adequacy in terms of computational complexity.Keywords: abstract argumentation frameworks; answer-set programming; implementation MotivationIn Artificial Intelligence (AI), the area of argumentation (the survey by Bench-Capon and Dunne (2007) gives an excellent overview) has become one of the central issues during the last decade. Argumentation provides a formal treatment for reasoning problems arising in a number of applications fields, including Multi-Agent Systems and Law Research. In a nutshell, the so-called abstract argumentation frameworks (AFs) formalise statements together with a relation denoting rebuttals between them, such that the semantics gives an abstract handle to solve the inherent conflicts between statements by selecting admissible subsets of them. The reasoning underlying such AFs turned out to be a very general principle capturing many other important formalisms from the areas of AI and knowledge representation.The increasing interest in argumentation led to numerous proposals for formalisations of argumentation. These approaches differ in many aspects. First, there are several ways as to how "admissibility" of a subset of statements can be defined; second, the notion of rebuttal has different meanings (or even additional relationships between statements are taken into account); finally, statements are augmented with priorities, such that the semantics yields those admissible sets which contain statements of higher priority. Thus, in order to compare these different proposals, it is desirable to have a system at hand, which is capable of dealing with a large number of argumentation semantics.Argumentation problems are, in general, intractable; for instance, deciding if an argument is contained in some preferred extension is known to be NP-complete. Therefore, developing dedicated algorithms for the different reasoning problems is non-trivial. A promising way to implement such systems is to use a reduction method, where the given problem is translated into another language, for which sophisticated systems already exist.

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“…3.1) in (García and Simari, 2004). Efstathiou and Hunter (2008) present an approach for generating arguments within the context of logical argumentation, using connection graphs (Kowalski, 1975) to optimize the search for arguments, where-as with (Besnard and Hunter, 2008)the support for a given claim consists of a minimal set of propositional formulas which together imply the claim.…”

Section: Related Workmentioning

confidence: 99%

Argument graphs and assumption-based argumentation

Craven

Toni

2016

Artificial Intelligence

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Arguments in structured argumentation are usually defined as trees, and extensions as sets of such treebased arguments with various properties depending on the particular argumentation semantics. However, these arguments and extensions may have redundancies as well as circularities, which are conceptually and computationally undesirable. Focusing on the specific case of Assumption-Based Argumentation (ABA), we propose novel notions of arguments and admissible/grounded extensions, both defined in terms of graphs. We show that this avoids the redundancies and circularities of standard accounts, and set out the relationship to standard tree-based arguments and admissible/grounded extensions (as sets of arguments). We also define new notions of graph-based admissible/grounded dispute derivations for ABA, for determining whether specific sentences hold under the admissible/grounded semantics. We show that these new derivations are superior with respect to standard dispute derivations in that they are complete in general, rather than solely for restricted classes of ABA frameworks. Finally, we present several experiments comparing the implementation of graph-based admissible/grounded dispute derivations with implementations of standard dispute derivations, suggesting that the graph-based approach is computationally advantageous.

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Algorithms for Effective Argumentation in Classical Propositional Logic: A Connection Graph Approach

Cited by 10 publications

References 15 publications

Argumentation Based on Classical Logic

Argumentation Based on Classical Logic

Answer-set programming encodings for argumentation frameworks

Argument graphs and assumption-based argumentation

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