Abstract
The introduction of explicit notions of rejection, or disbelief, in logics for knowledge representation can be justified in a number of ways. Motivations range from the need for versions of negation weaker than classical negation, to the explicit recording of classic belief contraction operations in the area of belief change, and the additional levels of expressivity obtained from an extended version of belief change which includes disbelief contraction. In this paper we present four logics of disbelief which address some or all of these intuitions. Soundness and completeness results are supplied and the logics are compared with respect to applicability and utility.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Alchourrón, C.E., Gärdenfors, P., Makinson, D.: On the logic of theory change: Partial meet functions for contraction and revision. Journal of Symbolic Logic 50, 510–530 (1985)
Caleiro, C., Carnielli, W.A., Coniglio, M.E., Sernadas, A., Sernadas, C.: Fibring non-truth-functional logics: Completeness preservation. Journal of Logic Language and Information 12(2), 183–211 (2003)
Chopra, S., Ghose, A., Meyer, T.: Non-prioritized ranked belief change. Journal of Philosophical Logic 32(3), 417–443 (2003)
Fuhrmann, A.: Theory contraction through base contraction. Journal of Philosophical Logic 20, 175–203 (1991)
Gärdenfors, P.: Knowledge in Flux: Modeling the Dynamics of Epistemic States. The MIT Press, Cambridge (1988)
Ghose, A., Goebel, R.: Belief states as default theories: Studies in non-prioritised belief change. In: Prade, H. (ed.) ECAI 1998. 13th European Conference on Artificial Intelligence, New York, pp. 8–12. John Wiley & Sons, Ltd., Chichester (1998)
Gomolińska, A.: On the logic of acceptance and rejection. Studia Logica 60, 233–251 (1998)
Gomolińska, A., Pearce, D.: Disbelief Change. In: Electronic essays on the occasion of the fiftieth birthday of Peter Gärdenfors (2001)
Guirevich, Y.: Intuitionistic logic with strong negation. Studia Logica 36, 49–59 (1977)
Hansson, S.-O.: Changes of disjunctively closed bases. Journal of Logic. Language and Information 2(4), 255–284 (1993)
Hughes, G.E., Cresswell, M.J.: An introduction to Modal Logic. Methuen, London (1972)
Reiter, R.: A logic for default reasoning. Artificial Intelligence 13, 81–132 (1980)
Rott, H.: Change, Choice and Inference. Oxford University Press, Oxford (1996)
Slupecki, J., Bryll, G., Wybraniec-Skardowska, U.: Theory of rejected propositions II. Studia Logica 30, 97–145 (1972)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Chopra, S., Heidema, J., Meyer, T. (2003). Some Logics of Belief and Disbelief. In: Gedeon, T.(.D., Fung, L.C.C. (eds) AI 2003: Advances in Artificial Intelligence. AI 2003. Lecture Notes in Computer Science(), vol 2903. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24581-0_31
Download citation
DOI: https://doi.org/10.1007/978-3-540-24581-0_31
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-20646-0
Online ISBN: 978-3-540-24581-0
eBook Packages: Springer Book Archive