Temporal reasoning with Abductive Event Calculus Marc Denecker
Lode Missiaen
Maurice Bruynooghe
Department of Computer Science, K.U.Leuven, Celestijnenlaan 200A, B-3001 Heverlee, Belgium. e-mail : fmarcd, lode,
[email protected]
Abstract.
We present the SLDNFA procedure, which integrates two important nonmonotonic paradigms, negation as failure and abduction. The main di erence between SLDNFA and existing approaches is the improved treatment of non-ground abductive goals. We present an extension for temporal reasoning based on Abductive Event Calculus. We show the power of the approach by applying it to planning and solving wellknown temporal reasoning problems. Interestingly, the procedure generates partial plans; the order of events is left unspeci ed when they do not interfere.
1 Introduction Temporal reasoning is an excellent domain for testing nonmonotonic reasoning techniques because of the frame problem : "the problem of representing the tendency of facts to endure over time" ([6]). Hanks and McDermott used the famous Yale turkey shooting problem (YTS) to show that well-known nonmonotonic reasoning systems failed to represent the frame axiom correctly. A nonmonotonic reasoning technique that was -mistakenly- not considered by these authors is negation as failure. It has been shown that the YTS representation in situation calculus or event calculus with negation as failure solves the problem correctly ([1], [4], [5]). Negation as failure alone is not sucient for representing many temporal reasoning problems. A major restriction is its incapacity of representing incomplete knowledge. The original event calculus only supports the prediction of a goal state, starting from a complete description of the initial state and the set of events. In many problems, the initial state or the events are not known. In planning, for example, the set of events is the subject of the search, and thus, a priori unknown. A solution to this problem is to extend event calculus with abduction ([3], [12]). In planning problems for example, the predicates which describe the events, i.e. happens=1; act=2 and
