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 $Λ^{sim}$ in the diamond language with each logic A 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.

Simulating Polyadic Modal Logics by Monadic Ones

PIAZZA, Carla;
2003

Abstract

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 $Λ^{sim}$ in the diamond language with each logic A 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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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11390/674445
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