LNint: A Temporal Logic that Combines Points and Intervals and the Absolute and Relative Approaches

The introduction of the temporal analysis in Logic has stimulated different approaches, some of them artificially opposed, such as to consider an absolute or relative nature of time, to consider points or intervals or to consider different time flows . . . In this paper we develop a temporal logic that combines these approaches to have a logic with a good computational behaviour. This logic, which we call LNint, is a modal logic that combines the treatment of points and intervals and declarations about dates and dated intervals like temporal logics with temporal arguments, or like reified logics and consequently, we obtain a mixture of the absolute and relative approaches to the treatment of time. LNint subsumes the US logic [12] and allows us not only to treat intervals with the operators of the logic proposed by Halpern and Shoham [14], but to define naturally operators like the chop presented by Moszkowski in [19] Moreover, the semantics of LNint can be extended, in a natural way, ..