Russell Greiner
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Abstract
Many tasks require “reasoning”—i.e., deriving conclusions from a corpus of explicitly stored information—to solve their range of problems. An ideal reasoning system would produce all-and-only the correct answers to every possible query, produce answers that are as specific as possible, be expressive enough to permit any possible fact to be stored and any possible query to be asked, and be (time) efficient. Unfortunately, this is provably impossible: as correct and precise systems become more expressive, they can become increasingly inefficient, or even undecidable. This survey first formalizes these hardness results, in the context of both logic- and probability-based reasoning, then overviews the techniques now used to address, or at least side-step, this dilemma.
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John Abel Moyne
The authors begin with the premise that many tasks require "reasoning"--i.e., deriving conclusions from a corpus of explicitly sotred information--to solve their range of problems. The paper is a useful survey and a formal mathematical description of various methodologies in reasoning: logical, probabilistic, expressive systems and methods of reducing expressiveness, imprecise logical and probabilistic reasoning, stochastic logical and probabilistic reasoning, and so forth. The authors admit that an ideal reasoning system, that would produce all and only the correct answers to every possible query, is not attainable. An ideal reasoning system has to be able to have an answer for all queries, and the answers have to be specific and expressive to permit facts to be stored. The problem is, according to the authors, that as correct and precise systems become more expressive, they can become inefficient. The authors propose various methods to overcome this dilemma, as far as possible. They summarize their procedure as, "[W]e have overviewed a large variety of techniques for improving the effectiveness of a reasoning system, considering both sound logical reasoners (focusing on Horn clauses), and probabilistic reasoners (focusing on belief nets). In general, these techniques embody some (perhaps implicit) tradeoff, where the system designer is willing to sacrifice some desirable property (such as expressiveness, precision, or correctness) to increase the system's efficiency..." (p. 23).
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