temporal logic

Galton, Antony, "Temporal Logic", The Stanford Encyclopedia of Philosophy (Fall 2008 Edition), Edward N. Zalta (ed.),
temporal logic

3.2 Determinism vs non-determinism

The choice of flow of time can be of philosophical significance. For example, one way of capturing the distinction between deterministic and non-deterministic theories is to model the former using a strictly linear flow of time, and the latter with a temporal structure which allows branching into the future. If we adopt the latter approach, then it is helpful in describing the semantics of tense and other operators to introduce the idea of a history, which is a maximal linearly-ordered set of instants. The branching future model will then stipulate that for any two histories there is an instant such that both histories share all the times up to and including that instant, but do not share any times after it. For each history containing a given instant, the times in that history which are later than the instant constitute a “possible future” for that instant.

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4.2 Applications in artificial intelligence

We have already mentioned the work of Allen (1984), which is concerned with finding a general framework adequate for all the temporal representations required by AI programs. The Event Calculus of Kowalski and Sergot (1986) is pursued more specifically within the framework of logic programming, but is otherwise similarly general in character. A useful survey of issues involving time and temporal reasoning in AI is Galton (1995), and a comprehensive recent coverage of the area is Fisher et al. (2005).

Much of the work on temporal reasoning in AI has been closely tied up with the notorious frame problem, which arises from the necessity for any automated reasoner to know, or be able to deduce, not only those properties of the world which do change as the result of any event or action, but also those properties which do not change. In everyday life, we normally handle such facts fluently without consciously adverting to them: we take for granted without thinking about it, for example, that the colour of a car does not normally change when one changes gear. The frame problem is concerned with how to formalise the logic of actions and events in such a way that indefinitely many inferences of this kind are made available without our having to encode them all explicitly. A seminal work in this area is McCarthy and Hayes (1969). A useful recent reference for the frame problem is Shanahan, 1997.