Pooling Modalities and Pointwise Intersection: Axiomatization and Decidability

Van De Putte, Frederik; Klein, Dominik

doi:10.1007/s11225-020-09901-6

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Published: 17 March 2020

Pooling Modalities and Pointwise Intersection: Axiomatization and Decidability

Studia Logica volume 109, pages 47–93 (2021)Cite this article

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Abstract

We establish completeness and the finite model property for logics featuring the pooling modalities that were introduced in Van De Putte and Klein (Pooling modalities and pointwise intersection: semantics, expressivity, and applications). The definition of our canonical models combines standard techniques with a so-called “puzzle piece construction”, which we first illustrate informally. After that, we apply it to the weakest classical logics with pooling modalities and investigate the technique’s potential for the axiomatization of stronger logics, obtained by imposing well-known frame conditions on the models.

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Acknowledgements

Open Access funding provided by Projekt DEAL. We are indebted to Eric Pacuit and Fengkui Ju for insightful discussions on the completeness proofs. We are also indebted to two anonymous referees for their incisive comments on an earlier version. Frederik Van De Putte’s work on this paper was supported by the European Comission through a Marie Skłodowska-Curie Fellowship (Grant Agreement ID: 795329) and by the Flemish Research Foundation (FWO-Vlaanderen). 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] 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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Authors and Affiliations

Philosophy Department, University of Bayreuth, Universitätsstraße 30, 95447, Bayreuth, Germany
Frederik Van De Putte & Dominik Klein
Department of Philosophy and Moral Science, Ghent University, Blandijnberg 2, 9000, Ghent, Belgium
Frederik Van De Putte
Political Science Department, University of Bamberg, Feldkirchenstraße 21, 96052, Bamberg, Germany
Dominik Klein

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Frederik Van De Putte
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Dominik Klein
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Correspondence to Frederik Van De Putte.

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Van De Putte, F., Klein, D. Pooling Modalities and Pointwise Intersection: Axiomatization and Decidability. Stud Logica 109, 47–93 (2021). https://doi.org/10.1007/s11225-020-09901-6

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Received: 06 June 2019
Published: 17 March 2020
Issue Date: February 2021
DOI: https://doi.org/10.1007/s11225-020-09901-6

Keywords

Pointwise intersection
Pooling modalities
Classical modal logics
Completeness
Finite model property
Puzzle piece construction