Many-Valued Modal Logic and Regular Equivalences in Weighted Social Networks

Abstract

Social network analysis is a methodology used extensively in social sciences. While classical social networks can only represent the qualitative relationships between actors, weighted social networks can describe the degrees of connection between actors. In classical social network, regular equivalence is used to capture the similarity between actors based on their linking patterns with other actors. Specifically, two actors are regularly equivalent if they are equally related to equivalent others. The definition of regular equivalence has been extended to regular similarity and generalized regular equivalence for weighted social networks. Recently, it was shown that social positions based on regular equivalence can be syntactically expressed as well-formed formulas in a kind of modal logic. Thus, actors occupying the same social position based on regular equivalence will satisfy the same set of modal formulas. In this paper, we will present analogous results for regular similarity and generalized regular equivalence based on many-valued modal logics.