The fluent calculus is a formalism for expressing dynamical domains in first-order logic

First-order logic

First-order logic is a formal logical system used in mathematics, philosophy, linguistics, and computer science. It goes by many names, including: first-order predicate calculus, the lower predicate calculus, quantification theory, and predicate logic...

. It is a variant of the situation calculus

Situation calculus

The situation calculus is a logic formalism designed for representing and reasoning about dynamical domains. It was first introduced by John McCarthy in 1963. The main version of the situational calculus that is presented in this article is based on that introduced by Ray Reiter in 1991...

; the main difference is that situations are considered representations of states. A binary function symbol is used to concatenate the terms that represent facts that hold in a situation. For example, that the box is on the table in the situation is represented by the formula . The frame problem

Frame problem

In artificial intelligence, the frame problem was initially formulated as the problem of expressing a dynamical domain in logic without explicitly specifying which conditions are not affected by an action. John McCarthy and Patrick J. Hayes defined this problem in their 1969 article, Some...

is solved by asserting that the situation after the execution of an action is identical to the one before but for the conditions changed by the action. For example, the action of moving the box from the table to the floor is formalized as:

This formula states that the state after the move is added the term and removed the term . Axioms specifying that is commutative and non-idempotent are necessary for such axioms to work.