Another Combination of Classical and Intuitionistic Conditionals release_zb5u37ddcndnvbh4vgxqhikitm

by Satoru Niki

Released as a article .

2022  

Abstract

On the one hand, classical logic is an extremely successful theory, even if not being perfect. On the other hand, intuitionistic logic is, without a doubt, one of the most important non-classical logics. But, how can proponents of one logic view the other logic? In this paper, we focus on one of the directions, namely how classicists can view intuitionistic logic. To this end, we introduce an expansion of positive intuitionistic logic, both semantically and proof-theoretically, and establish soundness and strong completeness. Moreover, we discuss the interesting status of disjunction, and the possibility of combining classical logic and minimal logic. We also compare our system with the system of Caleiro and Ramos.
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Date   2022-04-14
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arXiv  2204.06730v1
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