Abstract
First-order intuitionistic and classical Nelson–Wansing and Arieli–Avron–Zamansky logics, which are regarded as paradefinite and connexive logics, are investigated based on Gentzen-style sequent calculi. The cut-elimination and completeness theorems for these logics are proved uniformly via theorems for embedding these logics into first-order intuitionistic and classical logics. The modified Craig interpolation theorems for these logics are also proved via the same embedding theorems. Furthermore, a theorem for embedding first-order classical Arieli–Avron–Zamansky logic into first-order intuitionistic Arieli–Avron–Zamansky logic is proved using a modified Gödel–Gentzen negative translation. The failure of a theorem for embedding first-order classical Nelson–Wansing logic into first-order intuitionistic Nelson–Wansing logic is also shown.
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Acknowledgements
We would like to thank the anonymous referees for their valuable comments. This research was supported by JSPS KAKENHI Grant Numbers JP18K11171 and JP16KK0007 and Grant-in-Aid for Takahashi Industrial and Economic Research Foundation.
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Kamide, N. Embedding Friendly First-Order Paradefinite and Connexive Logics. J Philos Logic 51, 1055–1102 (2022). https://doi.org/10.1007/s10992-022-09659-3
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DOI: https://doi.org/10.1007/s10992-022-09659-3