Abstract
This chapter provides the foundations of the event calculus, formalism for commonsense reasoning. It reviews first-order logic and describe some notational conventions also discusses the basics of the event calculus. Furthermore, the chapter presents, axiomatizations of the event calculus (EC) and the discrete event calculus (DEC). The event calculus is based on first-order logic, which consists of a syntax, semantics, and proof theory. A language L of first-order logic is specified by disjoint sets of predicate symbols, function symbols, constants, and variables. Each predicate and function symbol has an arity. The semantics of a language L of first-order logic defines the meaning of a formula of L as the set of models of the formula or the set of structures in which the formula is true. In addition, the proof theory defines a proof of a formula π given a formula ψ as a sequence of formulas such that the last formula is π. The event calculus uses an extension of first-order logic called many-sorted first-order logic.
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