Logical Studies

Modal companions for some subintuitionistic logics

Document Type : Research

Author

Fatemeh Shirmohammadzadeh Maleki

Iranian Research Institute of Philosophy

https://doi.org/10.30465/lsj.2022.39376.1383
Abstract
Our main goal in this paper is to find modal companions for some subintuitionistic logics introduced by de Yongh and Shirmohammadzadeh. They introduced two types of neighbourhood frames, N-neighbourhood frames and NB-neighbourhood frames, in order to prove the completeness of these subintuitionistic logics. The structure of N-neighbourhood frames are similar to the neighborhood frames for non-normal modal logics. But the structure of NB- neighbourhood frames was introduced with a somewhat more complex definition than the neighbourhood semantics for non-normal modal logics. So in order to find out the modal companions of these subintuitionistic logics, we consider two types of translation, one from the language of intuitionistic propositional logic to the language of modal propositional logic, and the other from the language of intuitionistic propositional logic to the language of binary modal propositional logic, and compare the provability of a formula and its translation. Finally, using these two types of translations, we obtained the modal companions of desired subintuitionistic logics.

Keywords

Subintuitionistic Logic
Non-Normal Modal Logic
Binary Modal Logic
Modal Companion
Neighborhood Semantics
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Logical Studies
Volume 12, Issue 2
September 2021
Pages 149-173

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