Skip to main content Accessibility help
×
Home

CUMULATIVITY WITHOUT CLOSURE OF THE DOMAIN UNDER FINITE UNIONS

  • DOV M. GABBAY (a1) and KARL SCHLECHTA (a2)

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.

Copyright

Corresponding author

*DEPARTMENT OF COMPUTER SCIENCE KING'S COLLEGE LONDON STRAND, LONDON WC2R 2LS, UK E-mail:dov.gabbay@kcl.ac.uk
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:ks@cmi.univ-mrs.frkarl.schlechta@web.dehttp://www.cmi.univ-mrs.fr/~ks

References

Hide All
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), 119148.
Bossu, T., & Siegel, P. (1985). Saturation, nonmonotonic reasoning and the closed-world assumption. Artificial Intelligence, 25, 1363.
Gabbay, D., & Schlechta, K. (submitted). Reactive preferential structures and nonmonotonic consequence. hal-00311940, arXiv 0808.3075.
Gabbay, D., & Schlechta, K. (submitted). Roadmap for preferential logics. hal-00311941, arXiv 0808.3073.
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. 439457.
Kraus, S., Lehmann, D., & Magidor, M. (1990). Nonmonotonic reasoning, preferential models and cumulative logics. Artificial Intelligence, 44(1–2), 167207.
Lehmann, D. (1992a). Plausibility logic. In Boerger, J., and Kleine-Buening, R. editors. Proceedings CSL91. New York: Springer, pp. 227241.
Lehmann, F. (1992b) Plausibility logic. Technical Report TR-92-3. Hebrew University, Jerusalem, Israel.
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. 118.
Schlechta, K. (1996). Completeness and incompleteness for plausibility logic. Journal of Logic, Language and Information, 5(2), 177192[Dordrecht, The Netherlands: Kluwer].
Schlechta, K. (2004). Coherent Systems. Amsterdam, The Netherlands: Elsevier.
Shoham, Y. (1987). A semantical approach to nonmonotonic logics. In Proceedings Logics in Computer Science. Ithaca, NY.: IEEE Computer Society, pp. 275279, and In Proceedings IJCAI 87. pp. 388–392.

Related content

Powered by UNSILO

CUMULATIVITY WITHOUT CLOSURE OF THE DOMAIN UNDER FINITE UNIONS

  • DOV M. GABBAY (a1) and KARL SCHLECHTA (a2)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed.