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New techniques and completeness results for preferential structures

Published online by Cambridge University Press:  12 March 2014

Karl Schlechta
Karl Schlechta*
Affiliation:
Laboratoire d'informatique de Marseille, CNRS ESA 6077, CMI, Technopôle de Château-Gombert, F-13453 Marseille Cedex 13, France, E-mail: [email protected]
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Abstract

Preferential structures are probably the best examined semantics for nonmonotonic and deontic logics: in a wider sense, they also provide semantical approaches to theory revision and update, and other fields where a preference relation between models is a natural approach. They have been widely used to differentiate the various systems of such logics, and their construction is one of the main subjects in the formal investigation of these logics. We introduce new techniques to construct preferential structures for completeness proofs. Since our main interest is to provide general techniques, which can be applied in various situations and for various base logics (propositional and other), we take a purely algebraic approach, which can be translated into logics by easy lemmata, in particular, we give a clean construction via indexing by trees for transitive structures, this allows us to simplify the proofs of earlier work by the author, and to extend the results given there.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 65 , Issue 2 , June 2000 , pp. 719 - 746
Copyright
Copyright © Association for Symbolic Logic 2000

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References

REFERENCES

[ALS98-1]Audibert, L., Lhoussaine, C., and Schlechta, K., Distance based revision of preferential logics, to appear in the Logic Journal of the Interest Group in Pure and Applied Logics.Google Scholar
[BB94]Ben-David, Shai and Ben-Eliyahu, R., A modal logic for subjective default reasoning, Proceedings L1CS-94, (1994).Google Scholar
[BMP97]Bezzazi, H., Makinson, D., and Perez, R.P., Beyond rational monotony: Some strong non-Horn rules for nonmonotonic inference relations, Journal of Logic and Computation, vol. 7 (1997), no. 5, pp. 605–631.CrossRefGoogle Scholar
[BS85]Bossu, G. and Siegel, P., Saturation, nonmonotonic reasoning and the closed-world assumption, Artificial Intelligence, vol. 25 (1985), pp. 13–63.CrossRefGoogle Scholar
[Fr93]Freund, M., Supracompact inference operations, Studia Logica, vol. 52 (1994), pp. 457–481.CrossRefGoogle Scholar
[FL94]Freund, M. and Lehmann, D., Nonmonotonic reasoning: fromfinitary relations to infinitary inference operations, Studia Logica, vol. 53 (1994), pp. 161–201.CrossRefGoogle Scholar
[FH98]Friedman, N. and Halpern, J., Plausibility measures and default reasoning, Technical report, IBM Almaden Research Center, 1995, to appear in Journal of the ACM.Google Scholar
[Gab85]Gabbay, D. M., Theoretical foundations for non-monotonic reasoning in expert systems, Logics and Models of Concurrent Systems (Apt, K. R., editor), Springer, Berlin, 1985, pp. 439–457.CrossRefGoogle Scholar
[Han69]Hansson, B., An analysis of some deontic logics, Nous, vol. 3, pp. 373–398, Reprinted in R. Hilpinen ed. Deontic logic: Introductory and systematic readings, Reidel, Dordrecht 1971, pp. 121–147.CrossRefGoogle Scholar
[KLM90]Kraus, S., Lehmann, D., and Magidor, M., Nonmonotonic reasoning, preferential models and cumulative logics, Artificial Intelligence, vol. 44 (1-2) (1990), pp. 167–207.CrossRefGoogle Scholar
[LMS98-U]Lehmann, D., Magidor, M., and Schlechta, K., Distance semantics for belief revision, Technical report TR-98-10, Leibniz Center for Research in Computer Science, Institute of Computer Science, Hebrew University, Givat Ram, Jerusalem 91904, Israel, to appear in This Journal.CrossRefGoogle Scholar
[LM92]Lehmann, D. and Magidor, M., What does a conditional knowledge base entail?, Artificial Intelligence, vol. 55(1) (1992), pp. 1–60.CrossRefGoogle Scholar
[Lew73]Lewis, D., Counterfactuals, Blackwell, Oxford, 1973.Google Scholar
[Mak93]Makinson, D., Five faces of minimality, Studia Logica, vol. 52 (1993), pp. 339–379.CrossRefGoogle Scholar
[Mak94]Makinson, D., General patterns in nonmonotonic reasoning, Handbook of logic in artificial intelligence and logic programming (Gabbay, D., Hogger, C., and Robinson, , editors), Nonmonotonic and uncertain reasoning, vol. III, Oxford University Press, 1994, pp. 35–110.CrossRefGoogle Scholar
[Sch98-m3]Schlechta, K., A topological construction of a non-smooth model of cumulativity, to appear in Journal of Logic and Computation.Google Scholar
[Sch98-m4]Schlechta, K., Unrestricted preferential structures, to appear in Journal of Logic and Computation.Google Scholar
[Sch92]Schlechta, K., Some results on classical preferential models, Journal of Logic and Computation, vol. 2 (1992), no. 6, pp. 675–686.CrossRefGoogle Scholar
[Sch95-1]Schlechta, K., Defaults as generalized quantifiers, Journal of Logic and Computation, vol. 5 (1995), no. 4, pp. 473–494.CrossRefGoogle Scholar
[Sch95-3]Schlechta, K., Preferential choice representation theorems for branching time structures, Journal of Logic and Computation, vol. 5 (1995), pp. 783–800.CrossRefGoogle Scholar
[Sch96-3]Schlechta, K., Completeness and incompleteness for plausibility logic, Journal of Logic, Language and Information, vol. 5 (1996), pp. 177–192.CrossRefGoogle Scholar
[Sch96-1]Schlechta, K., Some completeness results for stoppered and ranked classical preferential models, Journal of Logic and Computation, vol. 6 (1996), no. 4, pp. 599–622.CrossRefGoogle Scholar
[Sch97-4]Schlechta, K., Filters and partial orders, Journal of the Interest Group in Pure and Applied Logics, vol. 5 (1997), no. 5, pp. 753–772.Google Scholar
[Sho87]Shoham, Yoav, A semantical approach to nonmonotonic logics, Proceedings of Logics in Computer Science, (1987), pp. 275–279.Google Scholar