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## Situation calculus and the real world

There have been many formulations of situation calculus.

[MH69] regarded a situation as a snapshot of the world at some instant of time. Such a system could not be known and described completely, but a person or program could know facts about a situation, i.e. the values of some fluents, and could infer some consequences of some actions from these facts. Situations are examples of rich entities, i.e. entities involving more detail than can be specified. Poor entities have finitely describable structures.

However, theories of action and change often use a more limited notion of situation. Thus Raymond Reiter [Rei01] and his colleagues regard situations as the nodes of a tree based at an initial situation S0 and whose edges branching from a situation s are the actions that may be taken in s. Other researchers, including Murray Shanahan [Sha97] and myself, use S0 as just a name for some situation whose consequences are of interest.

The viewpoint of this article is that a situation s is arbitrary element of a space Sits of situations, i.e. s bears the same relation to Sits as a group element bears to a group. Situation calculus theories relate situations, fluents and action by axioms, i.e. are abstract structures satisfying the theory.

A robot can use a poor situation calculus theory T to decide what to do in a world of rich situations. For example, the robot's blocks world theory may only allow specifying that one block is on another, not where it is located on the other. Suppose we have a mapping Observe from a subset of rich situations to poor situations. When the robot observes a world situation s to which the theory T applies, it obtains a poor situation . Using the theory T, the robot infers that a certain action a will advance its goal. It then performs an action Execute(a) in the world. If the theory T corresponds to the world properly, Result(Execute(a),s) will be an improved situation.

It isn't the purpose of this paper to develop a theory of the correspondence between rich real world situations and those of limited sitcalc domains. However, the way we formalize sitcalc is motivated by the hope of making these correspondences in a later theory.

Whether an event is external depends on the theory. If we can formulate when an event e will occur, then we can make our theory more powerful by including an occurrence axiom for that event. If we assume a deterministic world, the limiting case is a theory in which all events are internal.

Next: Elaboration tolerance Up: Actions and other events Previous: Actions and other events

John McCarthy
Fri Feb 8 17:29:20 PST 2002