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Logic and Logical Philosophy

Criteria causing inconsistencies. General gluts as opposed to negation gluts
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Criteria causing inconsistencies. General gluts as opposed to negation gluts

Authors

  • Diderik Batens Ghent University

DOI:

https://doi.org/10.12775/LLP.2003.001

Abstract

This paper studies the question: How should one handle inconsistencies that derive from the inadequacy of the criteria by which one approaches the world. I compare several approaches. The adaptive logics defined from CLuN appear to be superior to the others in this respect. They isolate inconsistencies rather than spreading them, and at the same time allow for genuine deductive steps from inconsistent and mutually inconsistent premises. Yet, the systems based on CLuN seem to introduce an asymmetry betweennegated and non-negated formulas, and this seems hard to justify. To clarify and understand the source of the asymmetry, the epistemological presuppositions of CLuN, viz. inadequate criteria, are investigated. This leads to a new type of paraconsistent logic that involves gluts with respect to all logical symbols. The larger part of the paper is devoted to this logic, to the adaptive logics defined from it, and to the properties of these systems. While the resulting logics are sensible and display interesting features, the search for variants of the justification leads to an unexpected justification for CLuN.

Author Biography

Diderik Batens, Ghent University

Centre for Logic and Philosophy of Science

References

Diderik Batens, ‘Paraconsistent extensional propositional logics’, Logique et Analyse, 90–91: 195–234, 1980.

Diderik Batens, ‘Dialectical dynamics within formal logics’, Logique et Analyse, 114: 161–173, 1986.

Diderik Batens, ‘Dynamic dialectical logics’, in Priest et al. [26], pp. 187–217.

Diderik Batens, ‘Inconsistency-adaptive logics’, in Or lowska [23], pp. 445–472.

Diderik Batens, ‘Linguistic and ontological measures for comparing the inconsistent parts of models’, Logique et Analyse, 165–166: 5–33, 1999. Appeared 2002.

Diderik Batens, ‘Zero logic adding up to classical logic’, Logical Studies, 2: 15, 1999, (Electronic Journal: http://www.logic.ru/LogStud/02/LS2.html).

Diderik Batens, ‘Rich inconsistency-adaptive logics. The clash between heuristic efficiency and realistic reconstruction’, in Francois Beets and Eric Gillet (eds.), Logique en perspective. Melanges offerts a Paul Gochet, pp. 513–543. Editions OUSIA, Brussels, 2000.

Diderik Batens, ‘Towards the unification of inconsistency handling mechanisms’, Logic and Logical Philosophy, 8: 5–31, 2000. Appeared 2002.

Diderik Batens, ‘On some remarkable relations between paraconsistent logics, modal logics, and ambiguity logics’, in Walter A. Carnielli, Marcelo E. Coniglio, and Itala M. Loffredo D’Ottaviano, (eds.), Paraconsistency. The Logical Way to the Inconsistent, pp. 275–293. Marcel Dekker, New York / Basel, 2002.

Diderik Batens, ‘The theory of the process of explanation generalized to include the inconsistent case’, Synthese, in print.

Diderik Batens, ‘A strengthening of the Rescher–Manor consequence relations’, Logique et Analyse, To appear.

Diderik Batens, ‘Narrowing down suspicion in inconsistent premise sets’, To appear in the Festschrift for Jerzy Perzanowski.

Diderik Batens and Kristof De Clercq, ‘A rich paraconsistent extension of full positive logic’, To appear.

Diderik Batens and Guido Vanackere, ‘Incompleteness-adaptive logics’, To appear.

Salem Benferhat, Didier Dubois, and Henri Prade, ‘Some syntactic approaches to the handling of inconsistent knowledge bases: A comparative study. Part 1: The flat case’, Studia Logica, 58:17–45, 1997.

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Guido Vanackere, ‘Minimizing ambiguity and paraconsistency’, Logique et Analyse, 165–166: 139–160, 1999. Appeared 2002.

Logic and Logical Philosophy

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Published

2003-11-23

How to Cite

1.
BATENS, Diderik. Criteria causing inconsistencies. General gluts as opposed to negation gluts. Logic and Logical Philosophy. Online. 23 November 2003. No. 11-12, pp. 5-37. [Accessed 6 July 2025]. DOI 10.12775/LLP.2003.001.
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