Mental Situation Calculus

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:

• Holds(p,s) is the assertion that the proposition p holds in the situation s. We shall mainly be interested in propositions p of a mental nature.
• Among the propositions that can hold are Know( p) and Believe(p), where p again denotes a proposition. Thus we can have

   

• As we will shortly see, sentences like

   

  are often useful. The sentence(7) asserts that the robot knows it doesn't know p.

• 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. The symbol mike denotes Mike himself, the function telephone takes a person into his telephone number. Thus telephone(mike) denotes Mike's telephone number. The symbol Mike is the concept of Mike, and the function Telephone takes a the concept of a person into the concept of his telephone number. Thus we distinguish between Mike's telephone number, denoted by telephone(mike) and the concept of his telephone number denoted by Telephone(Mike).

  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.