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Toward Efficient Default Reasoning
 Presented at the 4th International Workshop on Nonmonotonic Reasoning
, 1996
"... Early work on default reasoning aimed to formalize the notion of quickly "jumping to conclusions". Unfortunately, the resulting formalisms have proven more computationally complex than classical logics. This has dramatically limited the applicability of formal methods to real problems involving defa ..."
Abstract

Cited by 8 (2 self)
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Early work on default reasoning aimed to formalize the notion of quickly "jumping to conclusions". Unfortunately, the resulting formalisms have proven more computationally complex than classical logics. This has dramatically limited the applicability of formal methods to real problems involving defaults. The complexity of consistency checking is one of the two problems that must be addressed to reduce the complexity of default reasoning. We propose to approximate consistency checking using a novel synthesis of limited contexts and fast incomplete checks, and argue that this combination overcomes the limitations of its component parts. Our approach trades correctness for speed, but we argue that the nature of default reasoning makes this trade relatively inexpensive and intuitively plausible. We present a prototype implementation of a default reasoner based on these ideas, and a preliminary empirical evaluation. Computation and Nonmonotonicity Early work on nonmonotonic reasoning (NMR...
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"... Mundane, everyday, reasoning is fast. Given the inherent complexity of sound and complete reasoning with representations expressive enough to capture what people seem to know, commonsense reasoning must require shortcuts and assumptions. Some means of simplifying the retrieval of the inferential con ..."
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Mundane, everyday, reasoning is fast. Given the inherent complexity of sound and complete reasoning with representations expressive enough to capture what people seem to know, commonsense reasoning must require shortcuts and assumptions. Some means of simplifying the retrieval of the inferential consequences of a set of facts is obviously required. Instead of looking, as others have, at limited inference or syntactic restrictions on the representation, we explore the use of "vivid " forms for knowledge, in which determining the truth of a sentence is on the order of a database retrieval. In order to base a reasoning system on vivid knowledge, we consider ways to construct a vivid KB—a complete database of ground, atomic facts—given facts that may be presented in a more expressive language that allows incompleteness (e.g., firstorder logic). Besides offering an architecture for examining these problems, our results show that some forms of incomplete knowledge can still be handled efficiently if we extend a vivid KB in a natural way. Most interesting is the way that this approach trades accuracy for speed. 1
Toward Efficient Default Reasoning (Extended Abstract)
, 1992
"... ) David W. Etherington James M. Crawford AI Principles Research Department 600 Mountain Ave., P.O. Box 636 Murray Hill, NJ 079740636 fether, jcg@research.att.com Abstract Early work on default reasoning was motivated by the need to formalize the notion of "jumping to conclusions". Unfortunate ..."
Abstract
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) David W. Etherington James M. Crawford AI Principles Research Department 600 Mountain Ave., P.O. Box 636 Murray Hill, NJ 079740636 fether, jcg@research.att.com Abstract Early work on default reasoning was motivated by the need to formalize the notion of "jumping to conclusions". Unfortunately, most existing theories of default reasoning require explicitly considering every possible exceptional case before applying a default rule. They are thus inherently undecidable in the firstorder case, and remain intractable in all but the most restrictive cases. One possible approach to tractable default reasoning is to restrict consistency checks (which engender much of the intractability of default reasoning) to a restricted context. Unfortunately, consistency checking is undecidable in the firstorder case, so a small context in no way guarantees tractability. Another idea is to use linear or polynomial time, but incomplete, consistency checks. Unfortunately, the known tractable check...