Hypothetical Reasoning about Actions: From Situation Calculus to Event Calculus

Hypothetical reasoning about actions is the activity of preevaluating the effect of performing actions in a changing domain; this reasoning underlies applications of knowledge representation, such as planning and explanation generation. Action effects are often specified in the language of situation calculus, introduced by McCarthy and Hayes in 1969. More recently, the event calculus has been defined to describe actual actions, i.e., those that have occurred in the past, and their effects on the domain. Altough the two formalisms share the basic ontology of atomic actions and fluents, situation calculus cannot represent actual actions while event calculus cannot represent hypotethical actions. In this article, the language and the axioms of event calculus are extended to allow representing and reasoning about hypothetical actions, performed either at the present time or in the past, altough counterfactuals are not supported. Both event calculus and its extension are defined as logic programs so that theories are readily adaptable for Prolog query interpretation. For a reasonably large class of theories and queries, Prolog interpretation is shown to be sound and complete w.r.t. the main semantics for logic programs.