Monotonic Solution of The Frame Problem in The Situation Calculus

Abstract

The frame problem originally surfaced within McCarthy’s Situation Calculus [McCarthy68], when [McCarthy&Hayes69] applied it to reasoning about goal achievement. To illustrate their approach, they considered the problem of initiating a telephone conversation. They began by writing down plausible axioms which seemed to characterize the preconditions and effects of looking up a person’s telephone number and dialling that number. However, they found that they were still unable to prove that the plan “look up the number and dial it” would work, even if all the initial conditions were right (i.e., that the caller had a telephone and a telephone book, that the intended party was home, etc.). For example, the axioms provided no assurance that looking up the number would not make the caller’s telephone disappear, thus voiding a precondition for dialling.

“One feels that there should be some economical and principled way of succinctly saying what changes an action makes, without having to explicitly list all the things it doesn’t change as well; yet there doesn’t seem to be any other way to do it. That is the frame problem.”

Pat Hayes [Hayes87; p. 125]