A Modal Characterization of Granular Reasoning Based on Scott - Montague Models

Abstract

Granular reasoning proposed by Murai et al. is a mechanism for reasoning using granular computing, and the concept of ``focus" has been proposed as a key concept of granular reasoning. On the other hand, the authors have proposed another concept of granularity, called ``visibility". In this paper, we try to capture the concepts of visibility and focus as modalities of modal logics by introducing Scott-Montague models that illustrate the visibility and focus by modal operators, respectively.