Mental Situation Calculus

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## Mental Situation Calculus

The situation calculus, initiated in (McCarthy and Hayes 1969), is often used for describing how actions and other events affect the world. It is convenient to regard a robot's state of mind as a component of the situation and describe how mental events give rise to new situations. (We could use a formalism with a separate mental situation affected only by mental events, but this doesn't seem to be advantageous.) We contemplate a system in which what holds is closed under deductive inference, but knowledge is not.

The relevant notations are:

• is the assertion that the proposition holds in the situation . We shall mainly be interested in propositions of a mental nature.

• Among the propositions that can hold are and , where again denotes a proposition. Thus we can have

• As we will shortly see, sentences like

are often useful. The sentence(5) asserts that the robot knows it doesn't know .

• Besides knowledge of propositions we need a notation for knowledge of an individual concept, e.g. a telephone number. [McCarthy, 1979b] treats this in some detail. That paper has separate names for objects and concepts of objects and the argument of knowing is the latter. In that paper, the symbol denotes Mike himself, the function telephone takes a person into his telephone number. Thus denotes Mike's telephone number. The symbol is the concept of Mike, and the function takes a the concept of a person into the concept of his telephone number. Thus we distinguish between Mike's telephone number, denoted by and the concept of his telephone number denoted by . This enables us to say

to assert knowledge of Mike's telephone number and

to mean that the robot knows it doesn't know Mike's telephone number. The notation is somewhat ponderous, but it avoids the unwanted inference that the robot knows Mary's telephone number from the facts that her telephone number is the same as Mike's and that the robot knows Mike's telephone number. Having the sentence (7) in consciousness might stimulate the robot to look in the phone book.

Next: Mental Eventsespecially Up: Formalized Self-Knowledge Previous: Formalized Self-Knowledge

John McCarthy
Thu May 25 00:33:25 PDT 1995