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International Symposium on Methodologies for Intelligent Systems

ISMIS 1991: Methodologies for Intelligent Systems pp 570–579Cite as

Resolution and path dissolution in multiple-valued logics

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 542))

Abstract

Path dissolution is an inferencing mechanism for classical logic that efficiently generalizes the method of analytic tableaux. Two features that both methods enjoy are (in the propositional case) strong completeness and the ability to produce a list of essential models (satisfying interpretations) of a formula. The latter feature is particularly valuable in a setting in which one wishes to make use of satisfying interpretations rather than merely to determine whether any exist.

In this paper we describe a method for employing dissolution as a deduction mechanism for a class of multiple-valued logics that we call the UNF logics. The basic idea is to keep track of the sign of the formula. Dissolution is shown to be a sound rule of inference as well as strongly complete in this setting. We also describe how the signing technique may be used to apply resolution to these logics; Robinson's semantic tree argument is adapted to prove completeness.

This research was supported in part by the National Science Foundation under grants CCR-9005910 and CCR-9101208.

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Author information

Authors and Affiliations

  1. Inst. for Programming & Logics Dept. of Computer Science, State Univ. of N.Y. at Albany, 12222, Albany, NY

    Neil V. Murray

  2. Dept. of Mathematics, University of New Haven, 300 Orange Avenue, 06516, West Haven, CT

    Erik Rosenthal

Authors
  1. Neil V. Murray
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  2. Erik Rosenthal
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Editor information

Z. W. Ras M. Zemankova

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© 1991 Springer-Verlag Berlin Heidelberg

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Murray, N.V., Rosenthal, E. (1991). Resolution and path dissolution in multiple-valued logics. In: Ras, Z.W., Zemankova, M. (eds) Methodologies for Intelligent Systems. ISMIS 1991. Lecture Notes in Computer Science, vol 542. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-54563-8_120

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  • DOI: https://doi.org/10.1007/3-540-54563-8_120

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-54563-7

  • Online ISBN: 978-3-540-38466-3

  • eBook Packages: Springer Book Archive

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