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The finite model property for BCK and BCIW

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Abstract

This paper shows that both implicational logicsBCK andBCIW have the finite model property. The proof of the finite model property forBCIW, which is equal to the relevant logicR →, was originally given by the first author in his unpublished paper [6] in 1973. The finite model property forBCK can be obtained by modifying the proof of that forBCIW. Here, both of these proofs will be given in a unified form and the difference between them will be clarified. Further discussions will be given in the last section.

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Authors and Affiliations

  1. Centre for Information Science Research, I-Block, Australian National University, 2601, Canbera, ACT, Australia

    Robert K. Meyer

  2. School of Inform. Science, Japan Adv. Inst. of Science and Technology, Hokuriku, 923-12, Tatsunokuchi Ishikawa, Japan

    Hiroakira Ono

Authors
  1. Robert K. Meyer
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  2. Hiroakira Ono
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Additional information

The first author wishes to thank IIAS-SIS (Fujitsu Laboratories Ltd., Numazu) for 9 months hospitality in Japan, and for facilitating this research.

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Meyer, R.K., Ono, H. The finite model property for BCK and BCIW. Stud Logica 53, 107–118 (1994). https://doi.org/10.1007/BF01053025

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  • DOI: https://doi.org/10.1007/BF01053025

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