The situation calculus, initiated in [McCarthy, 1963] and [McCarthy and Hayes, 1969b], 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:
are often useful. The sentence(7) asserts that the robot knows it doesn't know p.
The convention used in this section of telephone and Telephone is different from the convention in the rest of the article of using capital letters to begin constants (whether individual, functional or predicate constants) and using symbols in lower case letters to denote variables.
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 (9) in consciousness might stimulate the robot to look in the phone book.