Pooling Modalities and Pointwise Intersection: Semantics, Expressivity, and Dynamics

Abstract

We study classical modal logics with pooling modalities, i.e. unary modal operators that allow one to express properties of sets obtained by the pointwise intersection of neighbourhoods. We discuss salient properties of these modalities, situate the logics in the broader area of modal logics (with a particular focus on relational seman- tics), establish key properties concerning their expressive power, discuss dynamic extensions of these logics and provide reduction axioms for the latter.