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

07 January 2022

Frederik Van De Putte & Dominik Klein

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  • Open Access
  • Published: 17 March 2020

Pooling Modalities and Pointwise Intersection: Axiomatization and Decidability

  • Frederik Van De Putte  ORCID: orcid.org/0000-0001-6828-01071,2 &
  • Dominik Klein  ORCID: orcid.org/0000-0002-7743-83991,3 

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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References

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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

  1. Philosophy Department, University of Bayreuth, Universitätsstraße 30, 95447, Bayreuth, Germany

    Frederik Van De Putte & Dominik Klein

  2. Department of Philosophy and Moral Science, Ghent University, Blandijnberg 2, 9000, Ghent, Belgium

    Frederik Van De Putte

  3. Political Science Department, University of Bamberg, Feldkirchenstraße 21, 96052, Bamberg, Germany

    Dominik Klein

Authors
  1. Frederik Van De Putte
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  2. 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

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Keywords

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