Step-Logic and the Three-Wise-Men Problem

Jennifer J. Elgot-Drapkin

The kind of resource limitation that is most evident in commonsense reasoners is the passage of time while the reasoner reasons. There is not necessarily any fixed and final set of consequences with which such a reasoning agent ends up. In formalizing commonsense reasoners, then, one must be able to take into account that time is passing as the reasoner is reasoning. The reasoner can then make use of such information in subsequent deductions. Step-logic is such a formalism. It was developed in [Elgot-Drapkin, 1988] to model the on-going process of deduction. Conclusions are drawn step-by-step. There is no "final" state of reasoning; the emphasis is on intermediate conclusions. In this paper we use step-logic to model the Three-wisemen Problem. Although others have formalized this problem, they have ignored the time aspect that is inherent in the problem: a correct assessment of the situation is made by recognizing that the reasoning process takes time and determining that the other wise men would have concluded such and such by now. This is an important aspect of the problem that needs to be addressed.

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