Empirical Negation, Co-Negation and the Contraposition Rule II: Proof-Theoretical Investigations

Niki, Satoru

doi:10.18778/0138-0680.2020.13

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2022

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“…L 4 is a syntactic of the logic TCC ω , introduced in [8], which in turn is a subsystem of the expansion of intuitionistic logic by empirical negation, IPC ∼ introduced in [4]. See also [16,17,18] for a comparison of these systems.…”

Section: Discussionmentioning

confidence: 99%

Another Combination of Classical and Intuitionistic Conditionals

Niki

Omori

2022

Electron. Proc. Theor. Comput. Sci.

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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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