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.
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We are greatly indebted to two anonymous referees for their incisive comments on earlier versions of this paper. Frederik Van De Putte’s research was funded by a Marie Skłodowska-Curie Fellowship (grant agreement ID: 795329), by a grant from the Research Foundation – Flanders (FWO-Vlaanderen), no. 12Q1918N, and by a grant from the Dutch Research Council (NWO), no. VI.Vidi.191.105. The work of Dominik Klein was partially supported by the Deutsche Forschungsgemeinschaft (DFG) and Agence Nationale de la Recherche (ANR) as part of the joint project Collective Attitude Formation [RO 4548/8-1], by DFG and Grantová Agentura České Republiky (GAČR) through the joint project From Shared Evidence to Group Attitudes [RO 4548/6-1], by DFG through the network grants Simulations of Social Scientific Inquiry  and Foundations, Applications and Theory of Inductive Logic , and by the National Science Foundation of China as part of the project Logics of Information Flow in Social Networks [17ZDA026].
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Van De Putte, F., Klein, D. Pooling Modalities and Pointwise Intersection: Semantics, Expressivity, and Dynamics. J Philos Logic 51, 485–523 (2022). https://doi.org/10.1007/s10992-021-09638-0
- Classical modal logics
- Pointwise intersection
- Pooling modalities
- Distributed information
- Information dynamics
- Power delegation