Semantics-based Nonmonotonic Inference
Heinrich Wansing
Source: Notre Dame J. Formal Logic Volume 36, Number 1
(1995), 44-54.
Abstract
In this paper we discuss Gabbay's idea of basing nonmonotonic deduction on semantic consequence in intuitionistic logic extended by a consistency operator and Turner's suggestion of replacing the intuitionistic base system by Kleene's three-valued logic. It is shown that a certain counterintuitive feature of these approaches can be avoided by using Nelson's constructive logic N instead of intuitionistic logic or Kleene's system. Moreover, in N a more general notion of consistency can be defined and nonmonotonic deduction can thus be based on a logical system satisfying the Deduction Theorem.
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Permanent link to this document: http://projecteuclid.org/euclid.ndjfl/1040308828
Mathematical Reviews number (MathSciNet): MR1359107
Digital Object Identifier: doi:10.1305/ndjfl/1040308828
Zentralblatt MATH identifier: 0839.03012
References
[1] Almukdad, A., and D. Nelson, ``Constructible falsity and inexact predicates," Journal of Symbolic Logic, vol. 49 (1984), pp. 231--233.
Mathematical Reviews (MathSciNet): MR86c:03020
Zentralblatt MATH: 0575.03016
JSTOR: links.jstor.org
Digital Object Identifier: doi:10.2307/2274105
[2] Clarke, M., ``Intuitionistic Non-Monotonic Reasoning---further results," pp. 525--527 in ECAI 88. Proceedings of the 8th European Conference on Artificial Intelligence, edited by Y. Kodratoff, Pitman, London, 1988.
[3] Clarke, M., and D. Gabbay, ``An Intuitionistic Basis for Non-Monotonic Reasoning," pp. 163--178 in Non-Standard Logics for Automated Reasoning, edited by P. Smets et al., Academic Press, London, 1988.
Mathematical Reviews (MathSciNet): MR1047257
[4] Došen, K., ``Intuitionistic Double Negation as a Necessity Operator," Publications de L'Institute Mathematique, vol. 49 (1984), pp. 15--20.
Mathematical Reviews (MathSciNet): MR87d:03041a
Zentralblatt MATH: 0555.03012
[5] Gabbay, D., ``Intuitionistic Basis for Non-Monotonic Logic," pp. 260--273 in Proceedings of the 6th Conference on Automated Deduction. Lecture Notes in CS 138, Springer-Verlag, Berlin, 1982.
Zentralblatt MATH: 0481.68091
Mathematical Reviews (MathSciNet): MR743446
Digital Object Identifier: doi:10.1007/BFb0000064
[6] Gurevich, Y., ``Intuitionistic Logic with Strong Negation," Studia Logica, vol. 36 (1977), pp. 49--59.
Mathematical Reviews (MathSciNet): MR58:160
Zentralblatt MATH: 0366.02015
Digital Object Identifier: doi:10.1007/BF02121114
[7] Jaspars, J., Calculi for Constructive Communication, PhD Thesis, University of Tilburg, 1994.
[8] Kripke, S., ``Semantical analysis of intuitionistic logic I," pp. 92--129 in Formal Systems and Recursive Functions, edited by J. Crossley and M. Dummett, North-Holland, Amsterdam, 1965.
Mathematical Reviews (MathSciNet): MR34:1184
Zentralblatt MATH: 0137.00702
[9] \mboxŁukaszewicz, W., Non-Monotonic Reasoning. Formalization of Commonsense Reasoning, Ellis Horwood, Chichester, 1990.
[10] McDermott D., and J. Doyle, ``Non-Monotonic Logic I," Journal of Artificial Intelligence, vol. 13 (1980), pp. 41--72.
Mathematical Reviews (MathSciNet): MR81j:03045
Zentralblatt MATH: 0435.68074
Digital Object Identifier: doi:10.1016/0004-3702(80)90012-0
[11] Pearce, D., ``Answer Sets and Constructive Logic, II: Extended Logic Programs and Related Non-monotonic Formalisms," pp. 457--475 in Logic Programming and Non-Monotonic Reasoning, edited by L. Pereira and A. Nerode, MIT Press, Cambridge (Massachusetts), 1993.
Mathematical Reviews (MathSciNet): MR96k:68024
[12] Pearce D., and G. Wagner, ``Logic Programming with Strong Negation," pp. 311--326 in Proceedings of the Workshop on Extensions of Logic Programming. Lecture Notes in AI 475, edited by P. Schroeder-Heister, Springer-Verlag, Berlin, 1990.
Mathematical Reviews (MathSciNet): MR1101610
Digital Object Identifier: doi:10.1007/BFb0038700
[13] Turner, R., Logics for Artificial Intelligence, Ellis Horwood, Chichester, 1984.
Mathematical Reviews (MathSciNet): MR87m:03002
[14] Wagner G., ``Logic Programming with Strong Negation and Inexact Predicates," Journal of Logic and Computation, vol. 1 (1991), pp. 835--859.
Mathematical Reviews (MathSciNet): MR1165249
Zentralblatt MATH: 0738.68018
Digital Object Identifier: doi:10.1093/logcom/1.6.835
[15] Wagner G., Vivid Logic. Knowledge-Based Reasoning with Two Kinds of Negation. Lecture Notes in AI 764, Springer-Verlag, Berlin, 1994.
Mathematical Reviews (MathSciNet): MR95h:68174
Zentralblatt MATH: 0806.68105
[16] Wansing, H., The Logic of Information Structures. Lecture Notes in AI 681, Springer-Verlag, Berlin, 1993.
Mathematical Reviews (MathSciNet): MR95b:03035
Zentralblatt MATH: 0788.03001
Notre Dame Journal of Formal Logic
