Instantiating abstract argumentation with classical logic arguments: Postulates and properties

Many proposals for logic-based formalisations of argumentation consider an argument as a pair ( , α), where the support is understood as a minimal consistent subset of a given knowledge base which has to entail the claim α. In case the arguments are given in the full language of classical propositional logic reasoning in such frameworks becomes a computationally costly task. For instance, the problem of deciding whether there exists a support for a given claim has been shown to be p 2 -complete. In order to better understand the sources of complexity (and to identify tractable fragments), we focus on arguments given over formulae in which the allowed connectives are taken from certain sets of Boolean functions. We provide a complexity classification for four different decision problems (existence of a support, checking the validity of an argument, relevance and dispensability) with respect to all possible sets of Boolean functions. Moreover, we make use of a general schema to enumerate all arguments to show that certain restricted fragments permit polynomial delay. Finally, we give a classification also in terms of counting complexity.

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Complexity of logic-based argumentation in Post's framework

Creignou¹,

Schmidt²,

Thomas³

et al. 2011

“…Nowadays, however, there is a growing body of work that models argumentation as inconsistency handling in either classical logic or some other standard deductive logic Hunter 2001, 2008;Amgoud and Cayrol 2002;Parsons, Wooldridge, and Amgoud 2003;Amgoud and Besnard 2009;Gorogiannis and Hunter 2011). In Pollock's terms, this work regards all reasons as deductive.…”

Section: A Critique Of Current Computational Models Of Argument In LImentioning

confidence: 99%

An appreciation of John Pollock's work on the computational study of argument

Prakken

Horty

2012

) was an influential American philosopher who made important contributions to various fields, including epistemology and cognitive science. In the last 25 years of his life, he also contributed to the computational study of defeasible reasoning and practical cognition in artificial intelligence. He developed one of the first formal systems for argumentation-based inference and he put many issues on the research agenda that are still relevant for the argumentation community today. This paper presents an appreciation of Pollock's work on defeasible reasoning and its relevance for the computational study of argument. In our opinion, Pollock deserves to be remembered as one of the founding fathers of the field of computational argument, while, moreover, his work contains important lessons for current research in this field, reminding us of the richness of its object of study.

“…Gorogiannis & Hunter 2011). Some of these are concerned with consistency of the set of premises (or set of claims) obtained from the arguments in an extension according to one of Dung's dialectical semantics.…”

Section: Arguments C ( ) = { α | ⊆ and α Is A Classical Argument}mentioning

confidence: 99%

“…We can represent the containment between the classical attack relations as above where an arrow from R 1 to R 2 indicates that R 1 ⊆ R 2 . For proofs, see Besnard & Hunter (2001) and Gorogiannis & Hunter (2011). flight cannot be both a low cost flight and a luxury flight.…”

Section: Counterarguments Based On Classical Logicmentioning

confidence: 99%

Constructing argument graphs with deductive arguments: a tutorial

Besnard¹,

Hunter²

2014

Self Cite

A deductive argument is a pair where the first item is a set of premises, the second item is a claim, and the premises entail the claim. This can be formalised by assuming a logical language for the premises and the claim, and logical entailment (or consequence relation) for showing that the claim follows from the premises. Examples of logics that can be used include classical logic, modal logic, description logic, temporal logic, and conditional logic. A counterargument for an argument A is an argument B where the claim of B contradicts the premises of A. Different choices of logic, and different choices for the precise definitions of argument and counterargument, give us a range of possibilities for formalising deductive argumentation. Further options are available to us for choosing the arguments and counterarguments we put into an argument graph. If we are to construct an argument graph based on the arguments that can be constructed from a knowledgebase, then we can be exhaustive in including all arguments and counterarguments that can be constructed from the knowledgebase. But there are other options available to us. We consider some of the possibilities in this review.