Year: 2026
Type: article
Abstract: We study interpretations of modal logics in one another where the Boolean connectives are interpreted identically and the modal operator diamond is interpreted by an arbitrary formula α(p).Clearly, such a formula α(p) defines an interpretation of a normal modal logic whenever α(p) is additive (that is, preserves disjunction) and normal (that is, preserves bottom) in the target logic.In the present paper, we provide a complete description of all additive and normal formulas in five prominent modal logics: K, GL, Grz, S4, and S5.For K, GL, and S5, we also describe all additive and normal formulas with parameters.
DOI: 10.4204/eptcs.447.18
Author: Lev V. Dvorkin
Institution: Lomonosov Moscow State University
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W7166454121
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