Skip to main content Accessibility help
×
Home

REACTIVE PREFERENTIAL STRUCTURES AND NONMONOTONIC CONSEQUENCE

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

Abstract

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.

Copyright

Corresponding author

*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

References

Hide All
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.
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. 5998.
Bossu, G., & Siegel, P. (1985). Saturation, nonmonotonic reasoning and the closed-world assumption. Artificial Intelligence, 25, 1363.
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, 321357.
Gabbay, D., & Schlechta, K. (2009). Roadmap for preferential logics. Journal of Applied Nonclassical Logic, 19(1), 4395. See also hal-00311941, arXiv 0808.3073.
Gabbay, D., & Schlechta, K. (to appear). Size and logic. Review of Symbolic Logic. See also arXiv 0903.1367.
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. 439457.
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. 720.
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. 155173.
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. 292341.
Gabbay, D. M. (to appear). Reactive Kripke models and contrary to duty obligations. Journal of Applied Logic, special issue on Deon-2008.
Gabbay, D. M., & Crochemore, M. (2008). Report, paper 304, Logic and Computation Group, Kings’s college, London, UK. July 2008, p. 21.
Kraus, S., Lehmann, D., & Magidor, M. (1990). Nonmonotonic reasoning, preferential models and cumulative logics. Artificial Intelligence, 44(1–2), 167207.
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, Milan, Italy, August 87, McDermott, J.P. ed., Morgan Kaufman 1987, San Francisco, pp. 388–392.

REACTIVE PREFERENTIAL STRUCTURES AND NONMONOTONIC CONSEQUENCE

  • 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.