Modal extension of ideal paraconsistent four-valued logic and its subsystem

Norihiro Kamide; Yoni Zohar

doi:10.1016/j.apal.2020.102830

Modal extension of ideal paraconsistent four-valued logic and its subsystem

Norihiro Kamide, Yoni Zohar

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

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Abstract

This study aims to introduce a modal extension M4CC of Arieli, Avron, and Zamansky's ideal paraconsistent four-valued logic 4CC as a Gentzen-type sequent calculus and prove the Kripke-completeness and cut-elimination theorems for M4CC. The logic M4CC is also shown to be decidable and embeddable into the normal modal logic S4. Furthermore, a subsystem of M4CC, which has some characteristic properties that do not hold for M4CC, is introduced and the Kripke-completeness and cut-elimination theorems for this subsystem are proved. This subsystem is also shown to be decidable and embeddable into S4.

Original language	English
Article number	102830
Journal	Annals of Pure and Applied Logic
Volume	171
Issue number	10
DOIs	https://doi.org/10.1016/j.apal.2020.102830
State	Published - Dec 2020
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2020 Elsevier B.V.

Funding

We would like to thank an anonymous referee for his or her valuable comments and suggestions. The idea of the translation function from M4CC into GS4 is a suggestion by the referee. Norihiro Kamide was supported by JSPS KAKENHI Grant Numbers JP18K11171 and JP16KK0007 .

Funders	Funder number
Japan Society for the Promotion of Science	JP18K11171, JP16KK0007

Keywords

Cut-elimination theorem
Embedding theorem
Gentzen-type sequent calculus
Ideal paraconsistent four-valued logic
Kripke-completeness theorem

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10.1016/j.apal.2020.102830

Cite this

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Modal extension of ideal paraconsistent four-valued logic and its subsystem

Abstract

Bibliographical note

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Keywords

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