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Intuitionistic and Constructive Modal Logics for Classical Modal Logicians
Abstract
This paper gives a survey of propositional modal logic in an intuitionistic setting. Mainly intended for readers already familiar with classical modal logic, we discuss why there are two prominent families of such logics, intuitionistic modal logics (IMLs) and constructive modal logics (CMLs), what motivates their study, and how they compare with each other. We then take a look at the logics lying between the CML and IML traditions, and survey various extensions and Diamond/Box-free fragments. We further record several observations which seem to be implicit or absent in the literature; we point out a small defect in the original semantics for CK and prove Lyndon interpolation theorems for CK and WK.
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BibTeX
@misc{sato2026intuitionistic,
title = {{Intuitionistic and Constructive Modal Logics for Classical Modal Logicians}},
author = {Yuta Sato},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2608.29708},
eprint = {2608.29708},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.29708},
}
RIS
TY - UNPB
TI - Intuitionistic and Constructive Modal Logics for Classical Modal Logicians
AU - Yuta Sato
PY - 2026
DA - 2026/10/09
PB - arXiv
DO - 10.48550/arxiv.2608.29708
UR - https://arxiv.org/abs/2608.29708
AB - This paper gives a survey of propositional modal logic in an intuitionistic setting. Mainly intended for readers already familiar with classical modal logic, we discuss why there are two prominent families of such logics, intuitionistic modal logics (IMLs) and constructive modal logics (CMLs), what motivates their study, and how they compare with each other. We then take a look at the logics lying between the CML and IML traditions, and survey various extensions and Diamond/Box-free fragments. We further record several observations which seem to be implicit or absent in the literature; we point out a small defect in the original semantics for CK and prove Lyndon interpolation theorems for CK and WK.
ER -