Hostname: page-component-7b7567c8c-wxvwp Total loading time: 0 Render date: 2026-11-14T08:03:17.759Z Has data issue: false hasContentIssue false
  • English
  • Français

REACTIVE PREFERENTIAL STRUCTURES AND NONMONOTONIC CONSEQUENCE

Published online by Cambridge University Press:  09 July 2009

DOV M. GABBAY and
KARL SCHLECHTA
DOV M. GABBAY*
Affiliation:
Department of Computer Science, King’s College London, and Department of Computer Science, Bar-Ilan University
KARL SCHLECHTA*
Affiliation:
Laboratoire d’Informatique Fondamentale de Marseille
*
*DEPARTMENT OF COMPUTER SCIENCE, KING’S COLLEGE LONDON, STRAND, LONDON WC2R 2LS, UK. E-mail: dov.gabbay@kcl.ac.uk, URL: http://www.dcs.kcl.ac.uk/staff/dg
†DEPARTMENT OF COMPUTER SCIENCE, BAR-ILAN UNIVERSITY, 52900 RAMAT-GAN, ISRAEL, 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.fr, karl.schlechta@web.de, URL: http://www.cmi.univ-mrs.fr/~ks
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.

We introduce Information Bearing Relation Systems (IBRS) as an abstraction of many logical systems. These are networks with arrows recursively leading to other arrows etc. We then define a general semantics for IBRS, and show that a special case of IBRS generalizes in a very natural way preferential semantics and solves open representation problems for weak logical systems. This is possible, as we can “break” the strong coherence properties of preferential structures by higher arrows, that is, arrows, which do not go to points, but to arrows themselves.

Information

Type
Research Article
Information
The Review of Symbolic Logic , Volume 2 , Issue 2 , June 2009, pp. 414 - 450
Copyright
Copyright © Association for Symbolic Logic 2009

References

BIBLIOGRAPHY

Barringer, H., Gabbay, D. M., & Rydeheard, D. (to appear). Reactive grammars. In Dershovitz, N., editor. Volume in Honour of Yakov Choueka. Lecture Notes in Computer Science. Springer.Google Scholar
Barringer, H., Gabbay, D. M., & Woods, J. (2005). Temporal dynamics of support and attack networks: From argumentation to zoology. In Hutter, D., Stephan, W., editors. Mechanizing Mathematical Reasoning, Volume Dedicated to Joerg Siekmann. Lecture Notes in Computer Science 2605. Berlin: Springer, pp. 59–98.CrossRefGoogle Scholar
Bossu, G., & Siegel, P. (1985). Saturation, nonmonotonic reasoning and the closed-world assumption. Artificial Intelligence, 25, 13–63.CrossRefGoogle Scholar
Dung, P. M. (1995). On the acceptability of arguments and its fundamental role in nonmonotonic reasoning, logic programming and n-person games. Artificial Intelligence, 77, 321–357.CrossRefGoogle Scholar
Gabbay, D., & Schlechta, K. (2009). Roadmap for preferential logics. Journal of Applied Nonclassical Logic, 19(1), 43–95. See also hal-00311941, arXiv 0808.3073.CrossRefGoogle Scholar
Gabbay, D., & Schlechta, K. (to appear). Size and logic. Review of Symbolic Logic. See also arXiv 0903.1367.Google Scholar
Gabbay, D. M. (1989). Theoretical foundations for non-monotonic reasoning in expert systems. In Apt, K. R., editor. Logics and Models of Concurrent Systems. Berlin: Springer, pp. 439–457.Google Scholar
Gabbay, D. M. (2004). Reactive Kripke semantics and arc accessibility. In Carnielli, W., Dionesio, F. M., Mateus, P. editors. Proceedings CombLog04. July 28–30, 2004. Centre of Logic and Computation, University of Lisbon, pp. 7–20.Google Scholar
Gabbay, D. M. (2008a). Reactive Kripke models and contrary to duty obligations. In van der Meyden, R., van der Torre, L., editors. DEON-2008, Deontic Logic in Computer Science. July 15–18, 2008, Luxembourg. Lecture Notes in Artificial Intelligence 5076. Berlin: Springer, pp. 155–173.CrossRefGoogle Scholar
Gabbay, D. M. (2008b). Reactive Kripke semantics and arc accessibility. In Avron, A., Dershowitz, N., Rabinovich, A., editors. Pillars of Computer Science: Essays Dedicated to Boris (Boaz) Trakhtenbrot on the Occasion of His 85th Birthday. Lecture Notes in Computer Science, Vol. 4800. Berlin: Springer, pp. 292–341.CrossRefGoogle Scholar
Gabbay, D. M. (to appear). Reactive Kripke models and contrary to duty obligations. Journal of Applied Logic, special issue on Deon-2008.Google Scholar
Gabbay, D. M., & Crochemore, M. (2008). Report, paper 304, Logic and Computation Group, Kings’s college, London, UK. July 2008, p. 21.Google Scholar
Kraus, S., Lehmann, D., & Magidor, M. (1990). Nonmonotonic reasoning, preferential models and cumulative logics. Artificial Intelligence, 44(1–2), 167–207.CrossRefGoogle 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, Milan, Italy, August 87, McDermott, J.P. ed., Morgan Kaufman 1987, San Francisco, pp. 388–392.Google Scholar