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.
Original language | English |
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Pages (from-to) | 549-571 |
Number of pages | 23 |
Journal | Studia Logica |
Volume | 108 |
Issue number | 3 |
DOIs | |
State | Published - 1 Jun 2020 |
Externally published | Yes |
Bibliographical note
Publisher Copyright:© 2019, Springer Nature B.V.
Funding
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).
Funders | Funder number |
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Japan Society for the Promotion of Science | JP18K11171, JP16KK0007 |
Keywords
- 4CC
- Completeness theorem
- Cut-elimination theorem
- Ideal paraconsistent four-valued logic