Simulating polyadic modal logics by monadic ones
G. Goguadze, C. Piazza, Y. Venema
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 in the diamond
language with each logic 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.
Keyword(s): modal logic, polyadic operators, interpretation,
simulation, transfer results