Towards the unification of inconsistency handling mechanisms
DOI:
https://doi.org/10.12775/LLP.2000.001Abstract
It is shown that the (flat) consequence relations defined from the Rescher-Manor Mechanism (that is: in terms of maximal consistent subsets of the premises) are all inconsistency-adaptive logics combined with a specific interpretation schema for the premises. Each of the adaptive logics is obtained by applying a suitable adaptive strategy to the paraconsistent logic CLuN.
This result provides all those consequence relations with a (dynamic) proof theory and with a static (as well as a dynamic) semantics.
References
Diderik Batens. Paraconsistent extensional propositional logics. Logique et Analyse, 90–91: 195–234, 1980.
Diderik Batens. Dynamic dialectical logics as a tool to deal with and partly eliminate unexpected inconsistencies. In J. Hintikka and F. Vandamme, editors, The Logic of Discovery and the Logic of Discourse, pages 263–271. Plenum Press, New York, 1985.
Diderik Batens. Dialectical dynamics within formal logics. Logique et Analyse, 114: 161–173, 1986.
Diderik Batens. Static and dynamic paraconsistent logics and their use in expert systems. CC-AI, 3:33–50, 1986.
Diderik Batens. Dynamic dialectical logics. In GrahamPriest, Richard Routley, and Jean Norman, editors, Paraconsistent Logic. Essays on the Inconsistent, pages 187–217. Philosophia Verlag, München, 1989.
Diderik Batens. Blocks. The clue to dynamic aspects of logic. Logique et Analyse, 150–152: 285–328, 1995. Appeared 1997.
Diderik Batens. Dynamic semantics applied to inconsistency-adaptive logics. In Logical Investigations, volume 5, pages 74–85. Moscow, “NAUKA”, 1998.
Diderik Batens. Inconsistency-adaptive logics. In Ewa Orłowska, editor, Logic at Work. Essays Dedicated to the Memory of Helena Rasiowa, pages 445–472. Physica Verlag (Springer), Heidelberg, New York, 1999.
Diderik Batens. Minimally abnormal models in some adaptive logics. Synthese, 125:5–18, 2000.
Diderik Batens. A survey of inconsistency-adaptive logics. In Batens et al. [13], pages 49–73.
Diderik Batens and Joke Meheus. A tableau method for inconsistency-adaptive logics. In Roy Dyckhoff, editor, Automated Reasoning with Analytic Tableaux and Related Methods, Lecture Notes in Artificial Intelligence Vol. 1847, pages 127–142. Springer, 2000.
Diderik Batens and Joke Meheus. Shortcuts and dynamic marking in the tableau method for adaptive logics. Studia Logica, 69:221–248, 2001.
Diderik Batens, Chris Mortensen, Graham Priest, and Jean Paul Van Bendegem, editors. Frontiers of Paraconsistent Logic. Research Studies Press, Baldock, UK, 2000.
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.
Kristof De Clercq. Two new strategies for inconsistency-adaptive logics. Logic and Logical Philosophy, in print.
Joke Meheus. Adaptive logic in scientific discovery: the case of Clausius. Logique et Analyse, 143–144:359–389, 1993. Appeared 1996.
Joke Meheus. An extremely rich paraconsistent logic and the adaptive logic based on it. In Batens et al. [13], pages 189–201.
Joke Meheus. Inconsistencies in scientific discovery. Clausius’s remarkable derivation of Carnot’s theorem. In Geert Van Paemel and et al., editors, Acta of the XXth International Congress of History of Science. Brepols, in print.
Graham Priest. Minimally inconsistent LP. Studia Logica, 50:321–331, 1991.
Nicholas Rescher. Hypothetical Reasoning. North-Holland, Amsterdam, 1964.
Nicholas Rescher. The Coherence Theory of Truth. Clarendon, Oxford, 1973.
Nicholas Rescher and Robert Brandom. The Logic of Inconsistency. A study in Non-Standard Possible-World Semantics and Ontology. Blackwell, Oxford, 1980.
Nicholas Rescher and Ruth Manor. On inference from inconsistent premises. Theory and Decision, 1:179–217, 1970.
Guido Vanackere. Ambiguity-adaptive logic. Logique et Analyse, 159:261–280, 1997. Appeared 1999.
Guido Vanackere. HL2. An inconsistency-adaptive and inconsistency-resolving logic for general statements that might have exceptions. Journal of Applied Non-Classical Logics, 10:317–338, 2000.
Guido Vanackere. Preferences as inconsistency-resolvers: the inconsistencyadaptive logic PRL. Logic and Logical Philosophy, in print.
Timothy Vermeir. Inconsistency-adaptive arithmetic. To appear.
Downloads
Published
How to Cite
Issue
Section
Stats
Number of views and downloads: 485
Number of citations: 0
