"The Event Calculus as a Linear Logic Program"
Vladimir Alexiev

http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.30.9953

Direct download:
http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.30.9953&rep=rep1&type=pdf

Abstract:

The traditional presentation of Kowalski's Event Calculus as a logic program uses
Negation-as-Failure (NAF) in an essential way to support persistence of fluents. 
In this paper we present an implementation of Event Calculus as a purely logical
(without NAF) Linear Logic (LL) program. This work demonstrates some of the
internal non-monotonic features of LL and its suitability for knowledge update
(as opposed to knowledge revision). Although NAF is an ontologically sufficient
solution to the frame problem, the LL solution is implementationally superior.
Handling of incomplete temporal descriptions and support for ramifications
(derived fluents) are also considered.