The Ramification Problem

Abstract

An invaluable advantage of action laws is that they allow to describe actions by their effects rather than by an exhaustive state transition table. However, the sole use of action laws quickly becomes unmanageable in complex domains, too. For action laws as they stand are supposed to be complete in that they specify the entire effect of an action. Yet although there are good reasons to assume that an action causes only a small number of direct changes, these in turn may initiate a long chain of indirect effects. Recall the action of toggling a switch, which, in the first place, causes nothing but a change of the switch’s position. However, the switch may be part of an electric circuit so that, say, some light bulb is turned off as a side effect, which in turn may cause someone to hurt himself in a suddenly darkened room by running against a chair that, as a consequence, falls into a television set whose implosion activates the fire alarm and so on and so forth.¹

A crucial question in this context concerns the distinction between indirect effects occurring during a single world’s state transition step and those which deserve separate state transitions (also called “delayed” effects). E.g., the above may not only be described as “the fire alarm is activated in the successor state after having closed the switch,” but also as, say, “the chair is falling in the successor state (and presumably hits the television set during the next state transition).” As a reasonable, albeit informal, guidance we suggest a single state transition should summarize what happens until some agent has the possibility to intervene by acting again (stopping the chair from falling, for instance). See also Section 2.7 for a discussion on indirect vs. delayed effects.