Nonmonotonic reasoning in temporal domains: The knowledge independence problem

Abstract

Much interest has been focused on nonmonotonic reasoning in temporal domains since Hanks and McDermott discovered that intuitive temporal representations give rise to the multiple extension problem. Here we consider nonmonotonic reasoning in temporal domains from the perspective of the Theorist hypothetical reasoning framework. We show how this framework can be applied to temporal reasoning in a simple and intuitive way to solve many of the problems posed in the recent literature, such as the Yale Shooting problem, Kautz's Vanishing Car problem, Haugh's Assassin problem, and Haugh's Robot problem.

The basis of our solution to these problems is the characterization of the notion that the past is independent of the future (temporal independence) and the provision of two additional modes of reasoning: conditional explanation and prediction. The problem of representing and reasoning about temporal independence is an instance of a more general problem which we call the knowledge independence problem. In this paper, we provide a preliminary definition of the knowledge independence problem; we leave to future work further development of the obvious connections with statistical independence. Using our preliminary definition, we show how to represent and reason about temporal independence and how this solves many temporal reasoning problems.