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Monotonic and nonmonotonic gentzen deduction systems for L3-valued propositional logic |
Cungen CAO1, Lanxi HU1,2( ), Yuefei SUI1,2 |
1. Key Laboratory of Intelligent Information Processing, Institute of Computing Technology, Chinese Academy of Sciences, Beijing 100190, China
2. School of Computer Science and Technology, University of Chinese Academy of Sciences, Beijing 100049, China |
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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 comultisequent 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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| Keywords
three-valued logic
multisequent
co-multisequent
monotonicity
Gentzen deduction system
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Corresponding Author(s):
Lanxi HU
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Issue Date: 27 January 2021
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