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.
and 
,
where again denotes a proposition. Thus we can have
are often useful. The sentence(5) asserts that the robot
knows it doesn't know .
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.
