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Logic and Logical Philosophy

Inconsistency-adaptive modal logics. On how to cope with modal inconsistency
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Inconsistency-adaptive modal logics. On how to cope with modal inconsistency

Authors

  • Hans Lycke Ghent University

DOI:

https://doi.org/10.12775/LLP.2010.003

Keywords

modal logics, paraconsistency, inconsistency-adaptive logics, inconsistency-adaptive modal logics

Abstract

In this paper, I will characterize a new class of inconsistency-adaptive logics, namely inconsistency-adaptive modal logics. These logics cope with inconsistencies in a modal context. More specifically, when faced with inconsistencies, inconsistency-adaptive modal logics avoid explosion, but still allow the derivation of sufficient consequences to adequately explicate the part of human reasoning they are intended for.

Author Biography

Hans Lycke, Ghent University

Centre for Logic and Philosophy of Scienc

References

Diderik Batens. “Inconsistency-adaptive logics”, pp. 445–472 in: E. Orłowska, editor, Logic at Work. Essays Dedicated to the Memory of Helena Rasiowa. Physica Verlag (Springer), Heidelberg, New York, 1999.

Diderik Batens, “A survey of inconsistency-adaptive logics”, pp. 49–73 in: D. Batens, C. Mortensen, G. Priest, and J.P. Van Bendegem, editors, Frontiers of Paraconsistent Logic. Research Studies Press, Baldock, UK, 2000.

Diderik Batens. “A general characterization of adaptive logics”, Logique et Analyse 173–175 (2001): 45–68.

Diderik Batens, “A strengthening of the Rescher-Manor consequence relations”, Logique et Analyse 183–184 (2003): 289–313.

Diderik Batens, “A universal logic approach to adaptive logics”, Logica Universalis 1 (2007): 221–242.

Diderik Batens. “Aspects of the dynamics of discussions and logics handling them”. To appear.

Diderik Batens and Kristof De Clercq, “A rich paraconsistent extension of full positive logic”, Logique et Analyse 185–188 (2004): 227–257.

Diderik Batens and Lieven Haesaert, “On classical adaptive logics of induction”, Logique et Analyse, 173–175 (2001): 255–290.

Diderik Batens and Joke Meheus, “Recent results by the inconsistency-adaptive labourers”, pp. 274–290 in: J.-Y. Béziau, W. Carnielli, and D. Gabbay, editors, Handbook of Paraconsistency. College Publications, London, 2007.

Diderik Batens, Joke Meheus, and Dagmar Provijn. “An adaptive characterization of signed systems for paraconsistent reasoning”. To appear.

Diderik Batens, Joke Meheus, Dagmar Provijn, and Liza Verhoeven, “Some adaptive logics for diagnosis”, Logic and Logical Philosophy 11–12 (2003): 39–65.

Marcelo Coniglio, “Logics for deontic inconsistency”, CLE e-prints, 7(4), 2007.

Richard Epstein. Semantic Foundations of Logic, vol. 1. Kluwer, Dordrecht, 1990.

Lou Goble, “Paraconsistent modal logic”, Logique et Analyse 193 (2006): 3–29.

Hans Lycke, “Fitch-style natural deduction for modal paralogics”, Logique et Analyse 207 (2009): 193–218.

Hans Lycke, Relevance in Reasoning. The Adaptive Logics Approach, PhD thesis, Ghent University, Gent, Belgium, 2007.

Joke Meheus, “An adaptive logic for pragmatic truth”, pp. 167–185 in: W. Carnielli, M. Coniglio, and I.M. Loffredo D’Ottaviano, editors, Paraconsistency. The Logical Way to the Inconsistent. Marcel Dekker, New York, 2002.

Joke Meheus, “Paraconsistent compatibility”, Logique et Analyse 183–184 (2003): 251–287.

Joke Meheus, “An adaptive logic based on Jaśkowski’s approach to paraconsistency”, Journal of Philosophical Logic 35 (2006): 539–567.

Graham Priest, “Logic of paradox”, Journal of Philosophical Logic 8 (1979): 219–241.

Graham Priest, An Introduction to Non-Classical Logic. Cambridge University Press, Cambridge, 2001.

Graham Priest, “Paraconsistent logic”, pp. 287–393 in: D. Gabbay and F. Guenthner, editors, Handbook of Philosophical Logic, vol. 6. Kluwer, Dordrecht/Boston/London, 2nd edition, 2002.

Giuseppe Primiero and Joke Meheus, “Majority merging by adaptive counting”, Synthese (KRA-series), 165 (2008): 203–223.

Logic and Logical Philosophy

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Published

2010-06-30

How to Cite

1.
LYCKE, Hans. Inconsistency-adaptive modal logics. On how to cope with modal inconsistency. Logic and Logical Philosophy. Online. 30 June 2010. Vol. 19, no. 1-2, pp. 31-61. [Accessed 3 July 2025]. DOI 10.12775/LLP.2010.003.
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