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Completeness and Cut-Elimination for First-Order Ideal Paraconsistent Four-Valued Logic

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Abstract

In this study, we prove the completeness and cut-elimination theorems for a first-order extension F4CC of Arieli, Avron, and Zamansky’s ideal paraconsistent four-valued logic known as 4CC. These theorems are proved using Schütte’s method, which can simultaneously prove completeness and cut-elimination.

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Acknowledgements

We would like to thank the anonymous referees for their valuable comments. Norihiro Kamide was supported by JSPS KAKENHI Grant Numbers JP18K11171, JP16KK0007 and JSPS Core-to-Core Program (A. Advanced Research Networks).

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Authors and Affiliations

  1. Department of Information and Electronic Engineering Faculty of Science and Engineering, Teikyo University, Toyosatodai 1-1, Utsunomiya, Tochigi, 320-8551, Japan

    Norihiro Kamide

  2. Computer Science Department, Stanford University, 353 Serra Mall, Stanford, CA, 94305, USA

    Yoni Zohar

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  1. Norihiro Kamide
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  2. Yoni Zohar
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Correspondence to Norihiro Kamide.

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Kamide, N., Zohar, Y. Completeness and Cut-Elimination for First-Order Ideal Paraconsistent Four-Valued Logic. Stud Logica 108, 549–571 (2020). https://doi.org/10.1007/s11225-019-09863-4

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