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Argumentation and Inconsistency-Tolerant Reasoning

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Abstract

This chapter is devoted to logical models for reasoning from contradictory information. It deals with methods, such as argumentation, that refrain from giving up any piece of information (by contrast with revision, as discussed in chapter “Main Issues in Belief Revision, Belief Merging and Information Fusion” of this volume). The baseline is to get the best, resorting to various possibilities, from the available information in order to reason in the most sensible way despite contradictions.

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Notes

  1. 1.

    Note that there exist other works, not described here, exploiting partial preorderings (Cayrol et al. 1993; Brewka 1994; Benferhat and Garcia 2002; Benferhat and Yahi 2012; Cayrol et al. 2014).

  2. 2.

    This ordering only depends on the stratum having the highest priority in which at least one formula has been removed for restoring consistency.

  3. 3.

    The subbases maximal for the preference based on set-inclusion are also called subtheories in (Brewka 1989) and correspond exactly to the strongly maximal consistent subbases of Dubois et al. (1991).

  4. 4.

    This principle consists in keeping among the credulous consequences only those such that their negation is not credulously inferred (Benferhat et al. 1993b). This inference is said argumentative.

  5. 5.

    Note that the Bo-preferred subbases are not presented here. Nevertheless all of them respect a common property: they contain the two formulae e and \(e \rightarrow b\) and so they entail e and b.

  6. 6.

    There are plenty of other references.

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Author information

Authors and Affiliations

  1. IRIT-CNRS, Université Paul Sabatier, Toulouse, France

    Leila Amgoud, Philippe Besnard, Claudette Cayrol & Marie-Christine Lagasquie-Schiex

  2. LRI, Université Paris-Sud-CNRS, Université Paris-Saclay, Orsay, France

    Philippe Chatalic

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  1. Leila Amgoud
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  2. Philippe Besnard
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  3. Claudette Cayrol
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  4. Philippe Chatalic
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  5. Marie-Christine Lagasquie-Schiex
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Correspondence to Leila Amgoud .

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Editors and Affiliations

  1. CRIL-CNRS, Université d'Artois and Institut Universitaire de France, Lens, France

    Pierre Marquis

  2. Aix Marseille Université, Université de Toulon, CNRS, LIS, Marseille, France

    Odile Papini

  3. IRIT, CNRS and Université Paul Sabatier, Toulouse, France

    Henri Prade

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Amgoud, L., Besnard, P., Cayrol, C., Chatalic, P., Lagasquie-Schiex, MC. (2020). Argumentation and Inconsistency-Tolerant Reasoning. In: Marquis, P., Papini, O., Prade, H. (eds) A Guided Tour of Artificial Intelligence Research. Springer, Cham. https://doi.org/10.1007/978-3-030-06164-7_13

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