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Allen's Interval Based Temporal Logic

Allen's theory of time and action [All83,All84] has intervals as primitive temporal elements and assumes a linear model of time. A set of thirteen mutually exclusive binary relations - $ \{ Equals$, $ Before$, $ After$, $ Meets$, $ MetBy$, $ Overlaps$, $ OverlappedBy$, $ Starts$, $ StartedBy$, $ During$, $ Contains$, $ Finishes$, $ FinishedBy \}$ - describe different ways of relating two convex intervals. In [AF94] all these thirteen relations are formally defined using the single primitive relation Meets. The logic has three types of temporal entities - properties, processes and events. These entities differ in the subintervals over which they hold.[*] Thus, properties are homogeneous, events are discrete and processes are either homogeneous or heterogeneous. The 2-place predicate - $ HOLDS(p, i)$ - specifies that property $ p$ holds over the interval $ i$. Another predicate - $ OCCUR(e, i)$ - denotes that an event $ e$ occurs over an interval $ i$. Finally, $ OCCURING(p, i)$ denotes that a process $ p$ occurs over an interval $ i$.



Darsana Josyula 2006-01-16