Propagating Possibilistic Temporal Constraints

The notion of time plays an important role in any intelligent activities Time is represented either im plicitly or explicitly We are interested in explicit representation of time The popular approaches for such representation are based on points or intervals or a hybrid of both Propositional temporal asser tions are represented as relations among the points or among the intervals The inde nite information among either the points or the intervals are repre sented as disjunctions In real world information is often incomplete imprecise uncertain and approximate Temporal knowledge is not an exception to this reality For example consider the following information John of ten drinks co ee during his breakfast Sometimes he drinks his co ee before the breakfast and drinks or ange juice during his breakfast There were few occa sions he drank water during his breakfast and drank co ee after the breakfast Mike talked to John over the phone while John was having co ee Suppose we are interested in nding out how Mik s telephone conversation was related to John s breakfast From the given information we have de nite relation be tween the telephone call and John s co ee but there is no information about the relationship between the co ee and the breakfast on that particular day In the absence of such information we can use John s habitual pattern to infer plausible relations Suppose Ic and Ib respectively represent the in terval over which John was having co ee and John was having breakfast Let It represents the interval over which Mike was having telephone conversation with John In interval logic the information is repre sented as It is during Ic and Ic is before or during or after Ib In such representation the disjunctive rela tions do not provide any clue about which relation is highly probable than the others Instead the repre sentation may let us believe that all the relations of a disjunction have equal probability for example hav ing co ee before during or after breakfast has equal probability This is not what the original informa tion tells us Based on John s habit having co ee during breakfast is much more probable than having co ee either before or after the breakfast This is sues have not been studied in temporal reasoning In this paper we will provide a representation to spec ify uncertain information and to propagate them over temporal constraint network