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UBC CS TR-90-09 Summary

Assumption Based Reasoning and Clause Management Systems, May 1990 Alex Kean and George K. Tsiknis

A {\em truth maintenance system} is a subsystem that manages the utilization of assumptions in the reasoning process of a problem solver. Doyle's original motivation for creating a truth maintenance system was to augment a reasoning system with a control strategy for activities concerning its non-monotonic state of beliefs. Hitherto, much effort has been invested in designing and implementing the concept of truth maintenance and little effort has been dedicated to the formalization that is essential to understanding it. This paper provides a complete formalization of the principle of truth maintenance. Motivated by Reiter and de Kleer's preliminary report on the same subject, this paper extends their study and gives a formal account of the concept of truth maintenance under the general title of {\em assumption based reasoning}. The concept of assumption based theory is defined and the notions of explanation and direct consequence are presented as forms of plausible conclusion with respect to this theory. Additionally, the concept of extension and irrefutable sentences are discussed together with other variations of explanation and direct consequence. A set of algorithms for computing these conclusions for a given theory are presented using the notion of prime implicates. Finally, an extended example on Boolean circuit diagnosis is shown to examplify these ideas.

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