Ramifications: An Extension and Correspondence Result for the Event Calculus

Classical logic Event Calculus, and the special purpose logical action language $\mathcal E$, 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 $\mathcal E$. 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 $\mathcal E$, and a proof of soundness and completeness of the EC-R theory with respect to $\mathcal E$'s model theoretic specification.