Algorithms for generating arguments and counterarguments in propositional logic

Efstathiou, Vasiliki; Hunter, Anthony

doi:10.1016/j.ijar.2011.01.005

Cited by 18 publications

(13 citation statements)

References 20 publications

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“…For instance, the nested sequent 1 ⇒ ( 2 ⇒ ψ) may be intuitively understood by 'if 1 were true, one would argue that 2 ⇒ ψ' and the hypersequent 1 ⇒ ψ 1 | 2 ⇒ ψ 2 may be understood (again, intuitively) as a disjunction, at the meta-level, of the arguments 21. Other techniques for generating arguments are considered, for example, in Besnard, Grégoire, Piette, and Raddaoui (2010) and Efstathiou & Hunter (2011).…”

Section: Conclusion and Further Workmentioning

confidence: 99%

Sequent-based logical argumentation

Arieli¹,

Straßer²

2015

Argument & Computation

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We introduce a general approach for representing and reasoning with argumentation-based systems. In our framework arguments are represented by Gentzen-style sequents, attacks (conflicts) between arguments are represented by sequent elimination rules, and deductions are made according to Dung-style skeptical or credulous semantics. This framework accommodates different languages and logics in which arguments may be represented, allows for a flexible and simple way of expressing and identifying arguments, supports a variety of attack relations (including those that reflect relevance or quantitative considerations), and is faithful to standard methods of drawing conclusions by argumentation frameworks. Altogether, we show that argumentation theory may benefit from incorporating proof theoretical techniques and that different non-classical formalisms may be used for backing up intended argumentation semantics.

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Section: Conclusion and Further Workmentioning

confidence: 99%

Sequent-based logical argumentation

Arieli¹,

Straßer²

2015

Argument & Computation

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“…The first one allows for the building of arguments [6]. The second one corresponds to abstract argumentation frameworks that model arguments as atomic entities, ignoring their internal structure and focusing on the interactions between arguments, or sets of arguments.…”

Section: Introductionmentioning

confidence: 99%

Bipolarity in Argumentation Graphs: Towards a Better Understanding

Cayrol

Lagasquie-Schiex

2011

Lecture Notes in Computer Science

134

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OATAO is an open access repository that collects the work of Toulouse researchers and makes it freely available over the web where possible. Any correspondance concerning this service should be sent to the repository administrator: staff-oatao@listes-diff.inp-toulouse.fr Bipolarity in argumentation graphs: Towards a better understanding Claudette Cayrol, Marie-Christine Lagasquie-Schiex * IRIT-UPS, Université de Toulouse, FranceA B S T R A C T Different abstract argumentation frameworks have been used for various applications within multi-agents systems. Among them, bipolar frameworks make use of both attack and support relations between arguments. However, there is no single interpretation of the support, and the handling of bipolarity cannot avoid a deeper analysis of the notion of support.In this paper we consider three recent proposals for specializing the support relation in abstract argumentation: the deductive support, the necessary support and the evidential support. These proposals have been developed independently within different frameworks. We restate these proposals in a common setting, which enables us to undertake a comparative study of the modellings obtained for the three variants of the support. We highlight relationships and differences between these variants, namely a kind of duality between the deductive and the necessary interpretations of the support.

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“…Furthermore, finding this set of formulae can substantially reduce the number of formulae that need to be considered for finding proofs for a claim, and therefore for finding arguments and canonical undercuts. Versions for full propositional logic, and for a subset of first-order logic, have been developed and implemented (Efstathiou & Hunter 2011).…”

Section: Automated Reasoning For Deductive Argumentationmentioning

confidence: 99%

Constructing argument graphs with deductive arguments: a tutorial

Besnard¹,

Hunter²

2014

Argument & Computation

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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.

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Algorithms for generating arguments and counterarguments in propositional logic

Cited by 18 publications

References 20 publications

Sequent-based logical argumentation

Sequent-based logical argumentation

Bipolarity in Argumentation Graphs: Towards a Better Understanding

Constructing argument graphs with deductive arguments: a tutorial

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