A unifying action calculus

McCarthy's Situation Calculus is arguably the oldest special-purpose knowledge representation formalism, designed to axiomatize knowledge of actions and their effects. Four decades of research in this area have led to a variety of alternative formalisms: While some approaches can be considered instances or extensions of the classical Situation Calculus, like Reiter's successor state axioms or the Fluent Calculus, there are also special planning languages like ADL and approaches based on a linear (rather than branching) time structure like the Event Calculus. The co-existence of many different calculi has two main disadvantages: The formal relations among them is a largely open issue, and a lot of today's research concerns the transfer of specific results from one approach to another. In this paper, we present a unifying action calculus, which encompasses (well-defined classes of) all of the aforementioned formalisms. Our calculus not only facilitates comparisons and translations between specific approaches, it also allows to solve interesting problems for various calculi at once. We exemplify this by providing a general, calculus-independent solution to a problem of practical relevance, which is intimately related to McCarthy's quest for elaboration tolerant formalisms: the modularity of domain axiomatizations