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Complexity of Many-valued Logics

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Beyond Two: Theory and Applications of Multiple-Valued Logic

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 114))

Abstract

As is the case for other logics, a number of complexity-related questions can be posed in the context of many-valued logic. Some of these, such as the complexity of the sets of satisfiable and valid formulas in various logics, are completely standard; others only make sense in a many-valued context. In this overview I concentrate on two kinds of complexity problems related to many-valued logic: first, I discuss the complexity of the membership problem in various languages, such as the satisfiable, respectively, the valid formulas in some well-known logics. Second, I discuss the size of representations of many-valued connectives and quantifiers, because this has a direct impact on the complexity of many kinds of deduction systems. I include results on both propositional and on first-order logic.

This article is an extended and revised version of an invited tutorial at ISMVL’01 [37]. It contains as well material from [36] in updated and revised form.

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Authors and Affiliations

  1. Dept. of Computing Science, Chalmers University of Technology, S-41296, Gothenburg, Sweden

    Reiner Hähnle

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  1. Department of Mathematics and Computer Science, Lehmann College, 250 Bedford Park Boulevard West, 10468-1589, Bronx, NY, USA

    Melvin Fitting

  2. National Institute of Telecommunications, ul. Szachowa 1, 04-894, Warsaw, Poland

    Ewa Orłowska

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Hähnle, R. (2003). Complexity of Many-valued Logics. In: Fitting, M., Orłowska, E. (eds) Beyond Two: Theory and Applications of Multiple-Valued Logic. Studies in Fuzziness and Soft Computing, vol 114. Physica, Heidelberg. https://doi.org/10.1007/978-3-7908-1769-0_9

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  • DOI: https://doi.org/10.1007/978-3-7908-1769-0_9

  • Publisher Name: Physica, Heidelberg

  • Print ISBN: 978-3-7908-2522-0

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