The Temporal Probabilistic (TP) Database management systems should provide support for valid-time indeterminacy of events, by proposing the concept of an indeterminate instant, that is, an interval of time-points (event's time-window) with an associated, lower and upper, probability distribution. In particular, users should be able to control, via query language constructs, the amount of temporal/probability approximation present in derived information. In this paper we present the new, equivalent to the denotational specification, the logic specification of TP-databases based on Constraint Logic Programs: TP-database can be seen as a deductive database with incomplete information, and, consequently, with a number of possible Herbrand models. We develop an epistemic extension of modal Temporal logic with the Kripke model semantics determined by Herbrand models of a TP-database also. Such modal language for events can be used to build the SQL-like query language extensions.
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