A functional approach for temporal $\times$ modal logics

Abstract.

This work is focused on temporal $\times$ modal logics. We study the representation of properties of functions of interest because of their possible computational interpretations. The semantics is exposed in an algebraic style, and the definability of the basic properties of the functions is analysed. We introduce minimal systems for linear time with total functions as well as with a class of partial functions (those with uniform domain). Moreover, completeness proofs are offered for these minimal systems. Finally, functional-validity is compared with $T\times W$-validity and Kamp-validity.