Simulating polyadic modal logics by monadic ones

Journal of Symbolic Logic 68 (2):419-462 (2003)
We define an interpretation of modal languages with polyadic operators in modal languages that use monadic operators (diamonds) only. We also define a simulation operator which associates a logic $\Lambda^{sim}$ in the diamond language with each logic Λ in the language with polyadic modal connectives. We prove that this simulation operator transfers several useful properties of modal logics, such as finite/recursive axiomatizability, frame completeness and the finite model property, canonicity and first-order definability
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DOI 10.2178/jsl/1052669058
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Natasha Kurtonina (1998). Categorial Inference and Modal Logic. Journal of Logic, Language and Information 7 (4):399-411.

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