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