A Real-time Solution to the Wise-men Problem

Honest-to-goodness commonsense reasoners have finite resources and hence also limited reasoning capabilities. Traditional logically complete logics therefore cannot be used to satisfactorily represent the reasoning of these agents. This observation has brought about tremendous strides in the area of limited reasoning. We mention here several such approaches. Konolige [Kon84] distinguishes three types of limited reasoning: relevance incompleteness, resourcelimited incompleteness, and fundamental logical incompleteness. Konolige uses the idea of relevance incompleteness, the notion that a reasoner may not know all the relevant rules in order to solve a problem, to get an interesting solution to the Three-wisemen problem (see [Kon84]). In this paper we present our own solution to this problem1, in which we focus on an aspect that Konolige has left unaddressed. The second type of limited reasoning that Konolige describes is that of resource-limited incompleteness: an agent may have the inferential capability to derive some consequence of his beliefs, yet does not have the computational resources to do so. This is a difficulty that arises, for instance, in a chess-playing program. The third and final type of limited reasoning that Konolige describes is that of fundamental logical