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Monotonic and nonmonotonic gentzen deduction systems for L3-valued propositional logic

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Abstract

A sequent is a pair (Γ, Δ), which is true under an assignment if either some formula in Γ is false, or some formula in Δ is true. In L3-valued propositional logic, a multisequent is a triple Δ|Θ|Γ, which is true under an assignment if either some formula in Δ has truth-value t, or some formula in Θ has truth-value m, or some formula in Γ has truth-value f. Correspondingly there is a sound and complete Gentzen deduction system G for multisequents which is monotonic. Dually, a co-multisequent is a triple Δ: Θ: Γ, which is valid if there is an assignment v in which each formula in Δ has truth-value ≠ t, each formula in Θ has truth-value ≠ m, and each formula in Γ has truth-value ≠ f. Correspondingly there is a sound and complete Gentzen deduction system G− for co-multisequents which is nonmonotonic.

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Authors and Affiliations

  1. Key Laboratory of Intelligent Information Processing, Institute of Computing Technology, Chinese Academy of Sciences, Beijing, 100190, China

    Cungen Cao, Lanxi Hu & Yuefei Sui

  2. School of Computer Science and Technology, University of Chinese Academy of Sciences, Beijing, 100049, China

    Lanxi Hu & Yuefei Sui

Authors
  1. Cungen Cao
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  2. Lanxi Hu
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  3. Yuefei Sui
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Corresponding author

Correspondence to Lanxi Hu.

Additional information

Cungen Cao graduated with a PhD degree from Institute of Mathematics Chinese Academy of Sciences, China. He is working at Key Laboratory of Intelligent Information Processing, Institute of Computing Technology, Chinese Academy of Sciences. He is a Professor, and PhD supervisor, a member of CCF. His main research interest is large-scale knowledge process.

Lanxi Hu got the Master’s degree from University of Chinese Academy of Sciences. She is studying in Key Laboratory of Intelligent Information Processing, Institute of Computing Technology, Chinese Academy of Sciences and University of Chinese Academy of Sciences, China, Engineer. Her main research interest is foundation of large-scale knowledge process.

Yuefei Sui graduated with a PhD degree from Institute of Software, Chinese Academy of Sciences, working at Key Laboratory of Intelligent Information Processing, Institute of Computing Technology, Chinese Academy of Sciences and University of Chinese Academy of Sciences, China. He is a Professor, and PhD supervisor, a member of CCF. His main research interests include foundation of large-scale knowledge process and mathematical logic.

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Cao, C., Hu, L. & Sui, Y. Monotonic and nonmonotonic gentzen deduction systems for L3-valued propositional logic. Front. Comput. Sci. 15, 153401 (2021). https://doi.org/10.1007/s11704-020-9076-2

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  • DOI: https://doi.org/10.1007/s11704-020-9076-2

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