A hybrid treatment of evolutionary sets

Abstract

This paper is about a synthesis of two quite different modal reasoning formalisms: the logic of subset spaces, and hybrid logic. Going beyond commonly considered languages we introduce names of objects involving sets and corresponding satisfaction operators, thus increase the expressive power to a large extent. The motivation for our approach is to logically model some general notions from topology like closeness, separation, and linearity, which are of fundamental relevance to spatial or temporal frameworks; in other words, since these notions represent basic properties of space and time we want them to be available to corresponding formal reasoning. We are interested in complete axiomatizations and effectivity properties of the associated logical systems, in particular.