On the Non-Monotonic Behavior of the Event Calculus for Deriving Maximal Time Intervals

The Event Calculus was proposed by Kowalski and Sergot as a simple and effective tool for dealing with time and actions in the framework of logic programming. In response to the occurrences of events, the formalism computes maximal and convex intervals of validity of the relationships holding in the modeled world. The case of interest is when the set of events is fixed, 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 effect, making previous intervals no longer derivable. As a consequence, a meaningful ordering over partially specified event orderings can not be based on inclusion of the corresponding Computed Interval sets. We introduce a monotonic version of the calculus and discuss how it relates to the original calculus; in particular, we discuss why it is not immediately viable for AI applications. To order partially specified orderings, however, we introduce a valuation function which chooses among alternative orderings the one(s) which minimizes the separation from the result obtainable by the monotonic version.