Multimodal logics for musical grammars

Abstract

Musical theory has often employed multiple grammars to formalize harmonic languages. We reinterpret a particular model in terms of a fusion of temporal and transitive modal logics. This work focuses on the analysis of typical decision problems of the field, while exploring how might the results vary according to the applied restrictions. In order to do so, we recur to well-known techniques and methods from computability theory and the field of modal logic. Some examples from the music-theoretic literature are presented and analyzed through the lenses of the considered results and observations.