Pooling Modalities and Pointwise Intersection: Axiomatization and Decidability

Frederik Van De Putte; Dominik Klein

doi:10.1007/s11225-020-09901-6

Pooling Modalities and Pointwise Intersection: Axiomatization and Decidability

Frederik Van De Putte, Dominik Klein

Research output: Contribution to journal › Article › Academic › peer-review

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.

Original language	English
Pages (from-to)	47-93
Number of pages	47
Journal	Studia Logica
Volume	109
Issue number	1
Early online date	17 Mar 2020
DOIs	https://doi.org/10.1007/s11225-020-09901-6
Publication status	Published - Feb 2021

Bibliographical note

Funding Information:
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].

Publisher Copyright:
© 2020, The Author(s).

Keywords

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

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Putte-Klein2021_Article_PoolingModalitiesAndPointwiseIFinal published version, 643 KBLicence: CC BY

Cite this

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title = "Pooling Modalities and Pointwise Intersection: Axiomatization and Decidability",

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{\textquoteright}s potential for the axiomatization of stronger logics, obtained by imposing well-known frame conditions on the models.",

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author = "{Van De Putte}, Frederik and Dominik Klein",

note = "Funding Information: 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{\textquoteright}s work on this paper was supported by the European Comission through a Marie Sk{\l}odowska-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 Grantov{\'a} Agentura {\v C}esk{\'e} Republiky (GA{\v C}R) 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]. Publisher Copyright: {\textcopyright} 2020, The Author(s).",

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Pooling Modalities and Pointwise Intersection: Axiomatization and Decidability

Abstract

Bibliographical note

Keywords

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