Real - Time Logics : Fictitious Clockas

In this paper we study two possible semantics for the real-time logic MTL (Metric Temporal Logic). In the rst semantics, called dense time semantics, time is modeled by the positive real numbers. In the second one, called ctitious clock semantics, real-time information is delivered by a global ctitious clock. We show that the ctitious clock semantics can be viewed as an abstraction of the dense time semantics. This abstraction relation is formalized by a parametric conservative connection. This formalization can be used to partially decide undecidable problems in the dense time semantics by reasoning on the ctitious clock semantics.