Criteria causing inconsistencies. General gluts as opposed to negation gluts

Diderik Batens



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.

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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:

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.

Salem Benferhat, Didier Dubois, and Henri Prade, ‘Some syntactic approaches to the handling of inconsistent knowledge bases: A comparative study. Part 2: The prioritized case’, in Or lowska [23], pp. 473–511.

David Lewis, Counterfactuals, Harvard University Press, Cambridge, Mass., 1973.

Witold Lukaszewicz, Non-Monotonic Reasoning. Formalization of Commonsense Reasoning, Ellis Horwood, New York, 1990.

Joke Meheus, ‘Adaptive logic in scientific discovery: the case of Clausius’, Logique et Analyse, 143–144:359–389, 1993. Appeared 1996.

Joke Meheus, Wetenschappelijke ontdekking en creativiteit. Een poging tot theorievorming op basis van een conceptuele, methodologische en logische studie, PhD thesis, Universiteit Gent (Belgium), 1997. Unpublished PhD thesis.

Joke Meheus, ‘An extremely rich paraconsistent logic and the adaptive logic based on it’, in Diderik Batens, Chris Mortensen, Graham Priest, and Jean Paul Van Bendegem, (eds.), Frontiers of Paraconsistent Logic, pp. 189–201, Research Studies Press, Baldock, UK, 2000.

Joke Meheus, ‘An adaptive logic based on Ja´ skowski’s D2’, To appear.

Ewa Orłowska, (ed.), Logic at Work. Essays Dedicated to the Memory of Helena Rasiowa, Physica Verlag (Springer), Heidelberg, New York, 1999.

Graham Priest, ‘Minimally inconsistent LP’, Studia Logica, 50:321–331, 1991.

Graham Priest, ‘Paraconsistent logic’, in D. Gabbay and F. Guenthner (eds.), Handbook of Philosophical Logic., volume 2. Kluwer, Dordrecht, 2 edition, in print.

Graham Priest, Richard Routley, and Jean Norman, (eds.), Paraconsistent Logic. Essays on the Inconsistent, Philosophia Verlag, München, 1989.

Nicholas Rescher, Hypothetical Reasoning, North-Holland, Amsterdam, 1964.

Nicholas Rescher, The Coherence Theory of Truth, Clarendon, Oxford, 1973.

Nicholas Rescher, Plausible Reasoning. An Introduction to the Theory and Practice of Plausibilistic Inference, Van Gorcum, Assen/Amsterdam, 1976.

Nicholas Rescher and Ruth Manor, ‘On inference from inconsistent premises’, Theory and Decision, 1: 179–217, 1970.

Peter K. Schotch and Raymond E. Jennings, ‘On detonating’, in Priest et al. [26], pp. 306–327.

Guido Vanackere, ‘Ambiguity-adaptive logic’, Logique et Analyse, 159: 261–280, 1997. Appeared 1999.

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

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