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Analysis of Case-Based Representability of Boolean Functions by Monotone Theory

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Algorithmic Learning Theory (ALT 1998)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 1501))

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Abstract

Classification is one of major tasks in case-based reasoning(CBR) and many studies have been done for analyzing properties of case-based classification [1,14,10,15,12,9,13,7]. However, these studies only consider numerical similarity measures whereas there are other kinds of similarity measure for diffierent tasks. Among these measures, HYPO system [2,3] in a legal domain uses a similarity measure based on set inclusion of diffierences of attributes in cases.

In this paper,we give an analysis of representability of boolean functions in case-based classification using the above set inclusion based similarity. We show that such case-based classification has a strong connection between monotone theory studied in [4,11]. Monotone theory is originated from computational learning theory and is used to show learnability of boolean function with polynomial DNF size and polynomial CNF size [4] and is used for deductive reasoning as well [11]. In this paper, we analyze a case-based representability of boolean functions by using the above relationship between the case-based classification by set inclusion based similarity and the monotone theory.We show that any boolean function is representable by a casebase whose size is bounded in polynomial of its DNF size and its CNF size and thus, k-term DNF, k-clause CNF can be efficiently representable in a casebase using set inclusion similarity.

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Author information

Authors and Affiliations

  1. Division of Electronics and Information, Hokkaido University, N13W8 Kita-ku, Sapporo, 060-8628, Japan

    Ken Satoh

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  1. Ken Satoh
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Editor information

Editors and Affiliations

  1. AG Künstliche Intelligenz - Expertensysteme, UniversitÄt Kaiserslautern, Postfach 3049, D-67653, Kaiserslautern, Germany

    Michael M. Richter

  2. Department of Computer Science, University of Maryland, College Park, MD, 20742, USA

    Carl H. Smith

  3. AG Algorithmischesn Lernen, UniversitÄt Kaiserslautern, Postfach 3049, D-67653, Kaiserslautern, Germany

    Rolf Wiehagen

  4. Graduate School of Information Science and Electrical Engineering Department of Informatics, Kyushu University, Kassuga, 816-8580, Japan

    Thomas Zeugmann

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© 1998 Springer-Verlag Berlin Heidelberg

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Satoh, K. (1998). Analysis of Case-Based Representability of Boolean Functions by Monotone Theory. In: Richter, M.M., Smith, C.H., Wiehagen, R., Zeugmann, T. (eds) Algorithmic Learning Theory. ALT 1998. Lecture Notes in Computer Science(), vol 1501. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-49730-7_14

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  • DOI: https://doi.org/10.1007/3-540-49730-7_14

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-65013-3

  • Online ISBN: 978-3-540-49730-1

  • eBook Packages: Springer Book Archive

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