GoKawiilFirst published Mon Feb 23, 2004; substantive revision Mon Feb 8, 2016
To most AI researchers, the frame problem is the challenge of representing the effects of action in logic without having to represent explicitly a large number of intuitively obvious non-effects. But to many philosophers, the AI researchers' frame problem is suggestive of wider epistemological issues. Is it possible, in principle, to limit the scope of the reasoning required to derive the consequences of an action? And, more generally, how do we account for our apparent ability to make decisions on the basis only of what is relevant to an ongoing situation without having explicitly to consider all that is not relevant?
The frame problem originated as a narrowly defined technical problem in logic-based artificial intelligence (AI). But it was taken up in an embellished and modified form by philosophers of mind, and given a wider interpretation. The tension between its origin in the laboratories of AI researchers and its treatment at the hands of philosophers engendered an interesting and sometimes heated debate in the 1980s and 1990s. But since the narrow, technical problem is largely solved, recent discussion has tended to focus less on matters of interpretation and more on the implications of the wider frame problem for cognitive science. To gain an understanding of the issues, this article will begin with a look at the frame problem in its technical guise. Some of the ways in which philosophers have re-interpreted the problem will then be examined. The article will conclude with an assessment of the significance of the frame problem today.
Put succinctly, the frame problem in its narrow, technical form is this (McCarthy & Hayes 1969). Using mathematical logic, how is it possible to write formulae that describe the effects of actions without having to write a large number of accompanying formulae that describe the mundane, obvious non-effects of those actions? Let's take a look at an example. The difficulty can be illustrated without the full apparatus of formal logic, but it should be borne in mind that the devil is in the mathematical details. Suppose we write two formulae, one describing the effects of painting an object and the other describing the effects of moving an object.
Colour(x, c) holds after Paint(x, c) Position(x, p) holds after Move(x, p)
Now, suppose we have an initial situation in which Colour(A, Red) and Position(A, House) hold. According to the machinery of deductive logic, what then holds after the action Paint(A, Blue) followed by the action Move(A, Garden)? Intuitively, we would expect Colour(A, Blue) and Position(A, Garden) to hold. Unfortunately, this is not the case. If written out more formally in classical predicate logic, using a suitable formalism for representing time and action such as the situation calculus (McCarthy & Hayes 1969), the two formulae above only license the conclusion that Position(A, Garden) holds. This is because they don't rule out the possibility that the colour of A gets changed by the Move action.
The most obvious way to augment such a formalisation so that the right common sense conclusions fall out is to add a number of formulae that explicitly describe the non-effects of each action. These formulae are called frame axioms. For the example at hand, we need a pair of frame axioms.
Colour(x, c) holds after Move(x, p) if Colour(x, c) held beforehand Position(x, p) holds after Paint(x, c) if Position(x, p) held beforehand
In other words, painting an object will not affect its position, and moving an object will not affect its colour. With the addition of these two formulae (written more formally in predicate logic), all the desired conclusions can be drawn. However, this is not at all a satisfactory solution. Since most actions do not affect most properties of a situation, in a domain comprising M actions and N properties we will, in general, have to write out almost MN frame axioms. Whether these formulae are destined to be stored explicitly in a computer's memory, or are merely part of the designer's specification, this is an unwelcome burden.
The challenge, then, is to find a way to capture the non-effects of actions more succinctly in formal logic. What we need, it seems, is some way of declaring the general rule-of-thumb that an action can be assumed not to change a given property of a situation unless there is evidence to the contrary. This default assumption is known as the common sense law of inertia. The (technical) frame problem can be viewed as the task of formalising this law.
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