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International Symposium on Abstraction, Reformulation, and Approximation

SARA 2002: Abstraction, Reformulation, and Approximation pp 178–195Cite as

Formalizing Approximate Objects and Theories: Some Initial Results

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 2371))

Abstract

This paper introduces some preliminary formalizations of the approximate entities of [McCarthy, 2000]. Approximate objects, predicates, and theories are considered necessary for human-level AI, and we believe they enable very powerful modes of reasoning (which admittedly are not always sound). Approximation is known as vagueness in philosophical circles and is often deplored as a defective aspect of human language which infects the precision of logic. Quite to the contrary, we believe we can tame this monster by formalizing it within logic, and then can “build solid intellectual structures on such swampy conceptual foundations.” [McCarthy, 2000].

We first introduce various kinds of approximation, with motivating examples. Then we develop a simple ontology, with minimal philosophical assumptions, in which to cast our formalization. We present our formalization, and show how it captures some ideas of approximation.

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Author information

Authors and Affiliations

  1. Stanford University, Stanford, CA, 94305, USA

    Aarati Parmar

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  1. Aarati Parmar
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Editor information

Editors and Affiliations

  1. College of Computing, Georgia Institute of Technology, 801 Atlantic Dr NW, Atlanta, GA, 30332-0280, USA

    Sven Koenig

  2. Department of Computing Science, Universtity of Alberta, 2-21 Athabasca Hall, Edmonton, Alberta, T6G 2E8, Canada

    Robert C. Holte

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© 2002 Springer-Verlag Berlin Heidelberg

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Parmar, A. (2002). Formalizing Approximate Objects and Theories: Some Initial Results. In: Koenig, S., Holte, R.C. (eds) Abstraction, Reformulation, and Approximation. SARA 2002. Lecture Notes in Computer Science(), vol 2371. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45622-8_14

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  • DOI: https://doi.org/10.1007/3-540-45622-8_14

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43941-7

  • Online ISBN: 978-3-540-45622-3

  • eBook Packages: Springer Book Archive

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