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Journal of Logic and Computation Advance Access originally published online on June 4, 2007
Journal of Logic and Computation 2007 17(4):639-685; doi:10.1093/logcom/exm018
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© The Author, 2007. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

Original Articles

Ramifications: An Extension and Correspondence Result for the Event Calculus

Jeremy Forth

Department of Computing, Imperial College London, 180 Queen's Gate, London SW7 2AZ, UK. E-mail: jforth{at}doc.ic.ac.uk

Rob Miller

S.L.A.I.S. University College London, Gower Street, London WC1E 6BT, UK. E-mail: rsm{at}ucl.ac.uk

Received 23 February 2006.


  Abstract

Classical logic Event Calculus, and the special purpose logical action language Formula, are both well established formalisms for describing actions and change. However, there is yet to be an account of ramifications in Event Calculus sufficiently general to represent the classes of domains expressible in Formula. Indeed, an adequately general ramification theory constructed in any general purpose logical language still awaits. Therefore, under the motivation of creating a flexible ramification theory in a universal language, suitable for integration into a rich action theory, a new enhanced version of classical logic Event Calculus named EC-R is proposed. EC-R supports representation and reasoning about domains containing ramifications for classes of domains more general than those possible under previous general purpose language formulations.

This article makes two main contributions. The first, EC-R, is a narrative-based action formalism able to represent concurrent events, non-deterministic actions and indirect causal effects by virtue of an integrated solution to the frame and ramification problems. The formalism can reason about significant subclasses of domains containing both mutually interacting effects and cyclic causal dependencies. The formalism is elaboration tolerant and may be integrated with the standard variants of the Event Calculus. The second contribution is the definition of a semantic mapping between EC-R and Formula, and a proof of soundness and completeness of the EC-R theory with respect to Formula's model theoretic specification.

Keywords: Event calculus; ramifications; action language; narrative


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