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A Three-Valued Fregean Quantification Logic

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Abstract

Kripke’s Fregean quantification logic FQ fails to formalize the usual first-order logic with identity due to the interpretation of the conditional operator. Motivated by Kripke’s syntax and semantics, the three-valued Fregean quantification logic FQ3 is proposed. This three valued logic differs from Kleene and Łukasiewicz’s three-valued logics. The logic FQ3 is decidable. A sound and complete Hilbert-style axiomatic system for the logic FQ3 is presented.

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Acknowledgements

Thanks are given to referees for their insightful and helpful comments on earlier versions of this paper.

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Authors and Affiliations

  1. Institute of Logic and Cognition, Department of Philosophy, Sun Yat-sen University, Guangzhou, China

    Minghui Ma

  2. Institute of Logic and Cognition, Sun Yat-sen University, Guangzhou, China

    Yuanlei Lin

Authors
  1. Minghui Ma
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  2. Yuanlei Lin
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Corresponding author

Correspondence to Minghui Ma.

Additional information

The first author was supported by the Project Supported by Guangdong Province (China) Pearl River Scholar Funded Scheme (2017–2019).

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Ma, M., Lin, Y. A Three-Valued Fregean Quantification Logic. J Philos Logic 48, 409–423 (2019). https://doi.org/10.1007/s10992-018-9469-y

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  • DOI: https://doi.org/10.1007/s10992-018-9469-y

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