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Injective models and disjunctive relations

Abstract : In this paper, we prove the existence of a one-to-one mapping between the set of all preferential inference relations defined on a language £ and a family of transitive relations among the elements of this language. Given a preferential inference relation, we use the corresponding transitive relation to define an order among the set of all worlds associated to £. We characterize all the preferential inference relations that can be represented by this ordered set. As a particular case, we study the family of disjunctive relations, that is relations where a conclusion drawn from a disjunction of premisses can be drawn from one at least of those premisses taken alone. We show that for this type of relation, the associated model is injective and filtered: if two worlds m and n satisfy a proposition α and are not minimal for that property, then there exists a world p less than both of them that satisfies α. As we prove, conversely, that any filtered model defines a disjunctive inference relation, we obtain a representation theorem for these relations. Applying finally these results to the family of rational relations, we get a new proof of the representation of these relations by means of ranked injective models.
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Contributor : Michael Freund <>
Submitted on : Thursday, February 21, 2013 - 2:02:01 PM
Last modification on : Tuesday, September 22, 2020 - 3:58:47 AM

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Michael Freund. Injective models and disjunctive relations. Journal of Logic and Computation, Oxford University Press (OUP), 1993, 3 (3), pp.231-247. ⟨10.1093/logcom/3.3.231⟩. ⟨halshs-00792045⟩



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