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SucheTemporal Operators on Partial Orders
B. Möller
In U.Berger, K.-H. Niggl, B. Reus (eds.): Proc. 3rd Domain
Workshop, Munich, 29--31 May 1997.
Institut für Informatik, LMU Munich, Technical Report 9712, December 1997, pp. 49-58
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. Box and diamond are viewed as standard modalities, which gives "half" of the standard axioms of LTL. Moreover, we show that the next-time operator 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.
Institut für Informatik, LMU Munich, Technical Report 9712, December 1997, pp. 49-58
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. Box and diamond are viewed as standard modalities, which gives "half" of the standard axioms of LTL. Moreover, we show that the next-time operator 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.