Modal and Temporal Operators on Partial Orders

We generalize the operators of classical linear time temporal logic to partial orders, such as the ones used in domain theory. This relates denotaional semantics and temporal logic. We put this into the general perspective of modal logic. a and b are viewed as standard modalities, which gives "half" of the standard axioms of LTL. Moroever, we show that the next-time operator c can be defined as a combination of two modalities. We show the role of the standard LTL axioms in narrowing the underlying partial orders to linear ones generated by the immediate-successor relation. We distinguish between modal and temporal validity of formulas and investigate their relation