Abstract
This volume of the Handbook of the Defeasible Reasoning and Uncertainty Management is about inconsistency and contradictions in logics. In order to provide a context for the volume, we briefly consider in this chapter some general issues of representing and reasoning with notions of contradiction and inconsistency. For the sake of generality in this chapter, logics are here understood as formal systems consisting of a language ℒ (in the form of a set of formulas) on which an inference operation C is defined. We will only consider syntactical accounts of inconsistency in the sequel. For a semantical approach to accounting for inconsistency, the reader could consider [Grant 1978].
This is a preview of subscription content, log in via an institution to check access.
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
Anderson A. R. and Belnap N. D. Jr. Entailment. The Logic of Relevance and Necessity. Princeton University Press, 1975.
Belnap N. D. Jr. A Useful Four-Valued Logic. In: Modern Uses of Multiple-Valued Logic, Dunn J. M. & Epstein G. (eds), pp. 8–37, Reidel, 1977.
Curry H. B. Foundations of Mathematical Logic. McGraw-Hill, New York, 1963.
Gabbay D. M. What is Negation in a System? Logic Colloquium ’ 86, Elsevier, Amsterdam, pp. 95–112, 1988.
Gabbay D. M. and Hunter A. Making Inconsistency Respectable. Funda-mentals of Logics in Artificial Intelligence Research, LNCS 535, pp.19–32, Springer-Verlag, 1991.
Gabbay D. M. and Wansing H. Negation in Structured Consequence Re-lations. In: Logic, Action, Information, Fuhrmann A. & Rott H. (eds), pp. 328–350, De Gruyter, 1995.
Grant J. Classifications for Inconsistent Theories. Notre Dame Journal of Formal Logic 19 (3), pp. 435–444, 1978.
Konolige K. On the Relation between Default and Autoepistemic Logic. Artificial Intelligence Journal 35, pp. 343–382, 1988.
Nelson D. Constructible Falsity. Journal of Symbolic Logic 14, pp. 16–26, 1949.
Reiter R. A Logic for Default Reasoning. Artificial Intelligence Journal 13, pp. 81–132, 1980.
Wansing, 1996] Wansing H. Negation. A Notion in Focus. De Gruyter, 1996.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1998 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Besnard, P., Hunter, A. (1998). Introduction to Actual and Potential Contradictions. In: Besnard, P., Hunter, A. (eds) Reasoning with Actual and Potential Contradictions. Handbook of Defeasible Reasoning and Uncertainty Management Systems, vol 2. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-1739-7_1
Download citation
DOI: https://doi.org/10.1007/978-94-017-1739-7_1
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-5063-2
Online ISBN: 978-94-017-1739-7
eBook Packages: Springer Book Archive