On the Non-monotonic Behavior of EventCalculus for Deriving Maximal Time IntervalsIliano Cervesato

The Event Calculus was proposed by Kowalski and Sergot as a simple and eeective tool for dealing with time and actions in the framework of logic programming 9]. In response to the occurrences of events, the formalism computes maximal and convex intervals of validity of the relationships holding in the mod-eled world. The case of interest is when the set of events is xed, but the order of their occurrence times is only partially known. The availability of new (pieces of) information about the relative order of events has a non-monotonic eeect, making previous intervals no longer derivable. As a consequence, a meaningful ordering over partially speciied event orderings may not be based on inclusion of the corresponding Computed Intervals sets. A monotonic version of the calculus is then proposed and compared to the original. We discuss why it is not immediately viable for AI applications, and show how it can be used to order partially speciied orderings. A valuation function is deened that chooses among alternative orderings the one(s) which minimizes the separation from the result obtainable by the monotonic version.