Abstract
In this paper, inspired in the field of belief revision, it is presented a novel operation for defining a new logic given a known logic. The operation consists in removing some (maybe undesirable) derived rule from a logic. Besides removing the ‘undesirable’ rule, this operation (called contraction) should change the logic in a minimal way. This paper presents formal definitions for contraction operations over logics, both as sets of rationality postulates and by means of concrete constructions. This allowed us to generalize several notions of maximality of logics presented in the literature. Furthermore, the proposed constructions are applied to the study of some paraconsistent and intermediate logics.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Arieli, O., Avron, A., Zamansky, A.: Maximally paraconsistent three-valued logics. In: Proceedings of the 12th International Conference on the Principles of Knowledge Representation and Reasoning (KR 2010), Toronto, Canada (2010)
Alchourrón, C., Gärdenfors, P., Makinson, D.: On the logic of theory change. Journal of Symbolic Logic 50(2), 510–530 (1985)
Alchourrón, C., Makinson, D.: Hierarchies of regulation and their logic. In: Hilpinen (ed.) New Studies in Deontic Logic, pp. 125–148. D. Reidel Publishing Company (1981)
Chagrov, A., Zakharyaschev, M.: Modal Logic. Oxford Logic Guides. Clarendon Press (1997)
D’Ottaviano, I.M.L., da Costa, N.C.A.: Sur un problème de Jaśkowski. Comptes Rendus de l’Académie de Sciences de Paris 270, 1349–1353 (1970)
Hansson, S.O.: Belief contraction without recovery. Studia Logica 50(2), 251–260 (1991)
Hansson, S.O.: A Textbook of Belief Dynamics. Kluwer Academic (1999)
Ribeiro, M.M.: Belief Revision in Non-Classical Logics. Springer Briefs in Computer Science, vol. XII. Springer (2012)
Sette, A.M., Carnielli, W.A.: Maximal weakly-intuitionistic logics. Studia Logica 55(1), 181–203 (1995)
Sette, A.M.: On the propositional calculus P1. Mathematica Japonicae 18, 173–180 (1973)
Wójcicki, R.: Theory of logical calculi: basic theory of consequence operations. Synthese library. Kluwer Academic Publishers (1988)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Ribeiro, M.M., Coniglio, M.E. (2012). Contracting Logics. In: Ong, L., de Queiroz, R. (eds) Logic, Language, Information and Computation. WoLLIC 2012. Lecture Notes in Computer Science, vol 7456. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32621-9_20
Download citation
DOI: https://doi.org/10.1007/978-3-642-32621-9_20
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-32620-2
Online ISBN: 978-3-642-32621-9
eBook Packages: Computer ScienceComputer Science (R0)