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An expressive three-valued logic with two negations

  • Logic for Artificial Intelligence I
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Methodologies for Intelligent Systems (ISMIS 1993)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 689))

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Abstract

Abstract This paper presents a flexible, expressive system K ∼3 of three-valued logic with two types of negation, having a sequent axiomatization which is an extension of the kind originally presented for Kleene's strong three-valued logic by Wang. The system K ∼3 turns out to be closely related to Lukasiewicz's three-valued logic. Applications: (1) Erik Sandewall has recently formulated a non-monotonic variant of three-valued logic. The non-monotonic “entailment” relation of his system can be expressed by a kind of “circumscription” formula in K ∼3 . (2) J. Shepherdson has suggested that a hybrid three-valued intuitionistic logic could be useful in connection with Kunen's modification of Fitting's three-valued version of the Clark Completion semantics for logic programs with negation. A suitable “intuitionistic fragment” of K ∼3 is obtained by allowing in proofs only sequents with at most one formula in the succedent.

Supported by Swedish agencies STU, STUF and TFR.

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Author information

Authors and Affiliations

  1. DSV, Stockholm University, Sweden

    Douglas R. Busch

  2. IDA, Linköping University, Sweden

    Douglas R. Busch

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  1. Douglas R. Busch
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Jan Komorowski Zbigniew W. Raś

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© 1993 Springer-Verlag Berlin Heidelberg

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Busch, D.R. (1993). An expressive three-valued logic with two negations. In: Komorowski, J., Raś, Z.W. (eds) Methodologies for Intelligent Systems. ISMIS 1993. Lecture Notes in Computer Science, vol 689. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-56804-2_3

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  • DOI: https://doi.org/10.1007/3-540-56804-2_3

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-56804-9

  • Online ISBN: 978-3-540-47750-1

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