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

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Frederik Van De Putte, Dominik Klein

Published: 2022, Last Modified: 24 Feb 2026J. Philos. Log. 2022EveryoneRevisionsBibTeXCC BY-SA 4.0
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 semantics), establish key properties concerning their expressive power, discuss dynamic extensions of these logics and provide reduction axioms for the latter.