Similarity-based graded modal logic

Abstract

Within the approximate reasoning Cramework, several systems oC modallogic have been proposed to formalize several kinds oC reasoning models ([MP94], [HM92], [FH91]). In particular, in [EGG95] a Kripke model-like theory for a logic of graded necessity and possibility operators is presented to model similarity-based reasoning. In this paper, we propose an axiomatization for this logic and we show that it is sound and complete with respect to classes oC models based where the accesibility relation is defined in terms of fuzzy similarity relations on the set oC possible worlds. Finally, we indicate how this logic can be used to characterize several graded entailments proposed in [DEG*95].