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Valuation structure

  • Zhaohui Zhu (a1) (a2), Zhenghua Pan (a3), Shifu Chen (a4) and Wujia Zhu (a5) (a6)

Abstract

This paper introduces valuation structures associated with preferential models. Based on KLM valuation structures, we present a canonical approach to obtain injective preferential models for any preferential relation satisfying the property INJ, and give uniform proofs of representation theorems for injective preferential relations appeared in the literature. In particular, we show that, in any propositional language (finite or infinite), a preferential inference relation satisfies INJ if and only if it can be represented by a standard preferential model. This conclusion generalizes the result obtained by Freund. In addition, we prove that, when the language is finite, our framework is sufficient to establish a representation theorem for any injective relation.

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[1]Bezzazi, H., Makinson, D., and Pérez, R. Pino, Beyond rational monotonicity: Some strong non-Horn rules for nonmonotonic inference relations, Journal of Logic and Computation, vol. 7 (1997), pp. 605631.
[2]Bezzazi, H. and Pérez, R. Pino, Rational transitivity and its models, Proceedings of the twenty-sixth international symposium on multiple-valued logic, IEEE Computer Society Press, 1996, pp. 160165.
[3]Freund, M., Injective models and disjunctive relations, Journal of Logic and Computation, vol. 3 (1993), pp. 231247.
[4]Gabbay, D. M., Theoretical foundation for nonmonotonic reasoning in expert systems, Proceedings of the NATO advanced study institute on logics and models of concurrent systems, LaColle-sur-loup, France (Apr, K. R., editor), Springer-Verlag, Berlin, 1985, pp. 439457.
[5]Kraus, S., Lehmann, D., and Magidor, M., Nonmonotonic reasoning, preferential models and cumulative logics, Artificial Intelligence, vol. 44 (1990), no. 1-2, pp. 167207.
[6]Lehmann, D. and Magidor, M., What does a conditional knowledge base entail?, Artificial Intelligence, vol. 55 (1992), pp. 160.
[7]Makinson, D., Handbook of logic in Artificial Intelligence and logic programming, vol. III, ch. 2, General patterns in nonmonotonic reasoning, Clarendon Press, Oxford, 1993.
[8]Pérez, R. Pino and Uzcátegui, Carlos, On representation theorems for nonmonotonic inference relation, to appear in this Journal, http://www.lif1.fr/GN0M/.
[9]Zhu, Zhaohui, Li, Bin, and Chen, Shifu, Valuation-ranked preferential model, The seventh international conference on principles of knowledge representation and reasoning (KR'2000), Breckenridge, Colorado, USA, April 11-15, 2000 (Cohn, A., Giunchilia, F., and Selman, B., editors), Morgan Kaufmann Publishers, 2000, pp. 647653.

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