A modal account of similarity-based reasoning

Abstract

One of the goals of a variety of approximate reasoning models is to cope with inference patterns more flexible than those of classical reasoning. Among them, similarity-based reasoning aims at modeling notions of resemblance or proximity among propositions and consequence relations which make sense in such a setting. One way of proceeding is to equip the set of interpretations or possible worlds with a similarity relation S, that is, a reflexive, symmetric, and t-norm-transitive fuzzy relation. We explore a modal approach to similarity-based reasoning, and we define three multi-modal systems with similarity-based Kripke model semantics. A similarity-based Kripke model is a structure 〈W, S, ‖ ‖〉, in which W is the set of possible worlds, ‖ ‖ represents an assignment of possible worlds to atomic formulas, and S is a similarity function S: W × W → G, where G is a subset of the unit interval [0,1] such that 0,1 ϵ G. We provide soundness and completeness results for these systems with respect to some classes of the above structures.