Monotonicity and nonmonotonicity in L3-valued propositional logic  

作　　者：Wei Li Yuefei Sui 

机构地区：[1]State Key Laboratory of Software Development Environment,Beihang University,Beijing,100083,China [2]Key Laboratory of Intelligent Information Processing,Institute of Computing Technology,Chinese Academy of Sciences,Beijing,100190,China [3]School of Computer Science and Technology,University of Chinese Academy of Sciences,Beijing,100049,China

出　　处：《Frontiers of Computer Science》2022年第4期33-43,共11页中国计算机科学前沿（英文版）

基　　金：supported by the Open Fund of the State KeyLaboratory of Sofware Development Environment(SKLSDE-2010KF-06);Beijing University of Aeronautics and Astronautics,and by the National Basic Research Program of China(973 Program)(2005CB321901).

摘　　要：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 L_(3)-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. There is a sound, complete and monotonic Gentzen deduction system G for sequents. Dually, there is a sound, complete and nonmonotonic Gentzen deduction system G′ for co-sequents Δ: Θ: Γ. By taking different quantifiers some or every, there are 8 kinds of definitions of validity of multisequent Δ∣Θ∣Γ and 8 kinds of definitions of validity of co-multisequent Δ: Θ: Γ, and correspondingly there are 8 sound and complete Gentzen deduction systems for sequents and 8 sound and complete Gentzen deduction systems for co-sequents. Correspondingly their monotonicity is discussed.

关 键 词：sequent mulisequent gentzen deduction system MONOTONICITY nonmonotonicity 

分 类 号：TP312[自动化与计算机技术—计算机软件与理论]