Frame problem

In artificial intelligence, 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. In a FOL system, additional axioms are required to make inferences about the environment (for example, that a block cannot change position unless it is physically moved). The frame problem is the problem of finding adequate collections of axioms for a viable description of a robot environment. In artificial intelligence, 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. In a FOL system, additional axioms are required to make inferences about the environment (for example, that a block cannot change position unless it is physically moved). The frame problem is the problem of finding adequate collections of axioms for a viable description of a robot environment. John McCarthy and Patrick J. Hayes defined this problem in their 1969 article, Some Philosophical Problems from the Standpoint of Artificial Intelligence. In this paper, and many that came after, the formal mathematical problem was a starting point for more general discussions of the difficulty of knowledge representation for artificial intelligence. Issues such as how to provide rational default assumptions and what humans consider common sense in a virtual environment. Later, the term acquired a broader meaning in philosophy, where it is formulated as the problem of limiting the beliefs that have to be updated in response to actions. In the logical context, actions are typically specified by what they change, with the implicit assumption that everything else (the frame) remains unchanged. The frame problem occurs even in very simple domains. A scenario with a door, which can be open or closed, and a light, which can be on or off, is statically represented by two propositions o p e n {displaystyle mathrm {open} } and o n {displaystyle mathrm {on} } . If these conditions can change, they are better represented by two predicates o p e n ( t ) {displaystyle mathrm {open} (t)} and o n ( t ) {displaystyle mathrm {on} (t)} that depend on time; such predicates are called fluents. A domain in which the door is closed and the light off at time 0, and the door opened at time 1, can be directly represented in logic by the following formulae: The first two formulae represent the initial situation; the third formula represents the effect of executing the action of opening the door at time 1. If such an action had preconditions, such as the door being unlocked, it would have been represented by ¬ l o c k e d ( 0 ) ⟹ o p e n ( 1 ) {displaystyle eg mathrm {locked} (0)implies mathrm {open} (1)} . In practice, one would have a predicate e x e c u t e o p e n ( t ) {displaystyle mathrm {executeopen} (t)} for specifying when an action is executed and a rule ∀ t . e x e c u t e o p e n ( t ) ⟹ o p e n ( t + 1 ) {displaystyle forall t.mathrm {executeopen} (t)implies mathrm {open} (t+1)} for specifying the effects of actions. The article on the situation calculus gives more details.