Logic for Computer Scientists/Modal Logic/Temporal Logics

Temporal Logics The two modalities and cannot be used to distinguish between past and future. For this we need a multi-modal logic with the following -operators : holds always in the future : holds always in the past : holds always and the corresponding -operators: : holds somewhere in the future : holds somewhere in the past : holds somewhere The semantics is then given as before, by giving constraints for the three reachability relations or by giving appropriate axioms, e.g. : Transitivity; an analog axiom holds for the two other -operators. : if we go from a time point in the future , we can go back in the past to the time point where was true. : connection of past with future. In addition there are many other aspects of temporal logics. E.g. one can distinguish between left- and rightlinear structures or between dense and discrete time structures.