Abstract

This paper generalises and complements the work on combining temporal logics started by Finger and Gabbay [11, 10]. We present proofs of transference of soundness, completeness and decidability for the temporalisation of logics T for any flow of time, eliminating the original restriction that required linear time for the transference of those properties through logic combination. We also generalise such results to the external application of a multi-modal system containing any number of connectives with arbitrary arity, that respect normality.This generalisation over generic flows of time propagates to other combinations of logics that can be interpreted in terms of temporalisations. In this way, the independent combination of temporal logics is studied over generic flows of time. We show the transfer of soundness, completeness and decidability for independent combination of temporal logics. Finally, we also discuss the independent combination of any finite number of normal multi-modal logics