actions: In the original formulation of the situation calculus, the initial situation, later denoted by , is not explicitly identified. The initial situation is not needed if situations are taken to be descriptions of the world. For example, to represent the scenario in which the door was closed but not locked and the action of opening it is performed is formalized by taking a constant to mean the initial situation and making statements about it (e.g., ). That the door is open after the change is reflected by formula being entailed. The initial situation is instead necessary if, like in the modern situation calculus, a situation is taken to be a history of actions, as the initial situation represents the empty sequence of actions. The version of the situation calculus introduced by McCarthy in 1986 differs to the original one for the use of functional fluents (e.g., is a term representing the position of in the situation ) and for an attempt to use circumscription to replace the frame axioms. The situation calculus as a logic program It is also possible (e.g. Kowalski 1979, Apt and Bezem 1990, Shanahan 1997) to write the situation calculus as a logic program: Here is a meta-predicate and the variable ranges over fluents. The predicates , and correspond to the predicates , , and respectively. The left arrow ← is half of the equivalence ↔. The other half is implicit in the completion of the program, in which negation is interpreted as negation as failure. Induction axioms are also implicit, and are needed only to prove program properties. Backward reasoning as in SLD resolution, which is the usual mechanism used to execute logic programs, implements regression implicitly. See also Frame problem Event calculus References J. McCarthy and P. Hayes (1969). Some philosophical problems from the standpoint of artificial intelligence. In B. Meltzer and D. Michie, editors, Machine Intelligence, 4:463–502. Edinburgh University Press, 1969. R. Kowalski (1979). Logic for Problem Solving - Elsevier North Holland. K.R. Apt and M. Bezem (1990). Acyclic Programs. In: 7th International Conference on Logic Programming. MIT Press. Jerusalem, Israel. R. Reiter (1991). The frame problem in the situation calculus: a simple solution (sometimes) and a completeness result for goal regression. In Vladimir Lifshitz, editor, Artificial intelligence and mathematical theory of computation: papers in honour of John McCarthy, pages 359–380, San Diego, CA, USA. Academic Press Professional, Inc. 1991. M. Shanahan