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CUMULATIVITY WITHOUT CLOSURE OF THE DOMAIN UNDER FINITE UNIONS

Published online by Cambridge University Press:  01 October 2008

DOV M. GABBAY  and
KARL SCHLECHTA
DOV M. GABBAY*
Affiliation:
Department of Computer Science, King's College London
KARL SCHLECHTA*
Affiliation:
Laboratoire d'Informatique Fondamentale de Marseille, UMR 6166, CNRS and Université de Provence
*
*DEPARTMENT OF COMPUTER SCIENCE KING'S COLLEGE LONDON STRAND, LONDON WC2R 2LS, UK E-mail:[email protected]
†LABORATOIRE D'INFORMATIQUE FONDAMENTALE DE MARSEILLE UMR 6166, CNRS AND UNIVERSITÉ DE PROVENCE CMI, 39, RUE JOLIOT-CURIE F-13453 MARSEILLE CEDEX 13, FRANCE E-mail:[email protected][email protected]http://www.cmi.univ-mrs.fr/~ks
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Abstract

For nonmonotonic logics, Cumulativity is an important logical rule. We show here that Cumulativity fans out into an infinity of different conditions, if the domain is not closed under finite unions.

Type
Research Article
Information
The Review of Symbolic Logic , Volume 1 , Issue 3 , October 2008 , pp. 372 - 392
Copyright
Copyright © Association for Symbolic Logic 2008

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References

BIBLIOGRAPHY

Arieli, O., & Avron, A. (2000). General patterns for nonmononic reasoning: from basic entailment to plausible relations. Logic Journal of the Interest Group in Pure and Applied Logics, 8(2), 119–148.Google Scholar
Bossu, T., & Siegel, P. (1985). Saturation, nonmonotonic reasoning and the closed-world assumption. Artificial Intelligence, 25, 13–63.CrossRefGoogle Scholar
Gabbay, D., & Schlechta, K. (submitted). Reactive preferential structures and nonmonotonic consequence. hal-00311940, arXiv 0808.3075.Google Scholar
Gabbay, D., & Schlechta, K. (submitted). Roadmap for preferential logics. hal-00311941, arXiv 0808.3073.Google Scholar
Gabbay, D. M. (1985). Theoretical foundations for non-monotonic reasoning in expert systems. In Apt, K. R., editor. Logics and Models of Concurrent Systems. Berlin, Germany: Springer, pp. 439–457.CrossRefGoogle Scholar
Kraus, S., Lehmann, D., & Magidor, M. (1990). Nonmonotonic reasoning, preferential models and cumulative logics. Artificial Intelligence, 44(1–2), 167–207.CrossRefGoogle Scholar
Lehmann, D. (1992a). Plausibility logic. In Boerger, J., and Kleine-Buening, R. editors. Proceedings CSL91. New York: Springer, pp. 227–241.Google Scholar
Lehmann, F. (1992b) Plausibility logic. Technical Report TR-92-3. Hebrew University, Jerusalem, Israel.Google Scholar
Makinson, D. (1989). General theory of cumulative inference. InReinfrank, M., de Kleer, J., Ginsberg, M.L., and Sandewall, E., editors. Non-Monotonic Reasoning, Proceedings 2nd International Workshop Grassau 1988. Berlin, Germany: Springer, pp. 1–18.Google Scholar
Schlechta, K. (1996). Completeness and incompleteness for plausibility logic. Journal of Logic, Language and Information, 5(2), 177–192[Dordrecht, The Netherlands: Kluwer].Google Scholar
Schlechta, K. (2004). Coherent Systems. Amsterdam, The Netherlands: Elsevier.Google Scholar
Shoham, Y. (1987). A semantical approach to nonmonotonic logics. In Proceedings Logics in Computer Science. Ithaca, NY.: IEEE Computer Society, pp. 275–279, and In Proceedings IJCAI 87. pp. 388–392.Google Scholar