Another Combination of Classical and Intuitionistic Conditionals
release_zb5u37ddcndnvbh4vgxqhikitm
by
Satoru Niki
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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