In artificial intelligence, a fluent is a condition that can change over time. In logical approaches to reasoning about actions, fluents can be represented in first-order logic by predicates having an argument that depends on time. For example, the condition "the box is on the table", if it can change over time, cannot be represented by ; a third argument is necessary to the predicate to specify the time: means that the box is on the table at time . This representation of fluents is modified in the situation calculus by using the sequence of the past actions in place of the current time.
A fluent can also be represented by a function, dropping the time argument. For example, that the box is on the table can be represented by , where is a function and not a predicate. In first order logic, converting predicates to functions is called reification; for this reason, fluents represented by functions are said to be reified. When using reified fluents, a separate predicate is necessary to tell when a fluent is actually true or not. For example, means that the box is actually on the table at time , where the predicate is the one that tells when fluents are true. This representation of fluents is used in the event calculus, in the fluent calculus, and in the features and fluents logics.
Some fluents can be represented as functions in a different way. For example, the position of a box can be represented by a function whose value is the object the box is standing on at time . Conditions that can be represented in this way are called functional fluents. Statements about the values of such functions can be given in first order logic with equality using literals such as . Some fluents are represented this way in the situation calculus.
From a historical point of view, fluents were introduced in the context of qualitative reasoning. The idea is to describe a process model not with mathematical equations but with natural language. That means an action is not only determined by its trajectory, but with a symbolic model, very similar to a text adventure.
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In artificial intelligence, with implications for cognitive science, the frame problem describes an issue with using first-order logic (FOL) to express facts about a robot in the world. Representing the state of a robot with traditional FOL requires the use of many axioms that simply imply that things in the environment do not change arbitrarily. For example, Hayes describes a "block world" with rules about stacking blocks together.
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. It is followed by sections about McCarthy's 1986 version and a logic programming formulation. The situation calculus represents changing scenarios as a set of first-order logic formulae.
The fluent calculus is a formalism for expressing dynamical domains in first-order logic. It is a variant of the situation calculus; 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 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.
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