A semantic characterization of disjunctive relations

Abstract

We study here some semantic properties of a specific kind of preferential relations, those which satisfy the rule of Disjunctive Rationality. This rule means essentially that if one may draw a conclusion from a disjunction of premisses, then one should be able to draw this conclusion from at least one of these premisses taken alone.

The main result we obtain in this paper is the construction of a representation theorem for such relations. We show indeed that there exists a certain kind of models which induce precisely all preferential operations satisfying the rule of Disjunctive Rationality. These models themselves reveal to be particularly easy to handle. They are just subsets of the set of all worlds of the language supporting the given relation, equipped with an ordering which is filtered: if two worlds n and m satisfy a proposition x and are not minimal for that property, then there exists a world p less than m and less than n that satisfies x.