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Knowledge and Information Systems

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13.06.2018 | Regular Paper

A formal characterization of the outcomes of rule-based argumentation systems

verfasst von: Leila Amgoud, Philippe Besnard

Erschienen in: Knowledge and Information Systems | Ausgabe 1/2019

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Abstract

Rule-based argumentation systems are developed for reasoning about defeasible information. As a major feature, their logical language distinguishes between strict rules (encoding strict information) and defeasible rules (describing general behavior with exceptional cases). They build arguments by chaining such rules, define attacks between them, use a semantics for evaluating the arguments and finally identify the plausible conclusions that follow from the rules. Focusing on the family of inconsistency-based attack relations, this paper presents the first study of the outcomes of such systems under various acceptability semantics, namely naive, stable, semi-stable, preferred, grounded and ideal. It starts by extending the existing list of rationality postulates that any rule-based system should satisfy. Then, it defines the key notion of option of a theory (a theory being a set of facts, a set of strict rules and a set of defeasible rules). For each of the cited semantics, it characterizes the extensions of a rule-based system that satisfies all the postulates in terms of options of the theory under which the system is built. It also fully characterizes the set of plausible conclusions of the system. The results show that designing a rule-based argumentation system requires great care.

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There is an apparent asymmetry between s and \(\lnot s\) but it is meaningless because we can choose an atom t to represent the intuitive statement formalized by \(\lnot s\) and then the intuitive statement formalized by s gets represented as \(\lnot t\). As an illustration about numbers, by letting odd instead of even, or vice versa, to be an atom of \({\mathcal {L}}\), asymmetry about negation could be reversed, while in both cases the meaning would be the same.

Let \({\mathcal {T}}\) be a theory. \(\mathtt {Free}({\mathcal {T}})\) is a sub-theory (X, Y, Z) of \({\mathcal {T}}\) such that for all minimal conflict \(C = (X', Y', Z')\) of \({\mathcal {T}}\), it holds that \(X \cap X' = \emptyset \) and \(Y \cap Y' = \emptyset \) and \(Z \cap Z' = \emptyset \). A minimal conflict of theory \({\mathcal {T}}\) is a sub-theory C of \({\mathcal {T}}\) such that \(\mathtt {CN}(C)\) is inconsistent and \(\not \exists C' \sqsubset C\) such that \(\mathtt {CN}(C')\) is inconsistent.

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Titel: A formal characterization of the outcomes of rule-based argumentation systems
verfasst von: Leila Amgoud
Philippe Besnard
Publikationsdatum: 13.06.2018
Verlag: Springer London
Erschienen in: Knowledge and Information Systems / Ausgabe 1/2019
Print ISSN: 0219-1377
Elektronische ISSN: 0219-3116
DOI: https://doi.org/10.1007/s10115-018-1227-5

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