Monotonicity and nonmonotonicity in L<sub>3</sub>-valued propositional logic

doi:10.1007/s11704-021-0382-0

Front. Comput. Sci.

2022, Vol. 16

Issue (4) : 164315 https://doi.org/10.1007/s11704-021-0382-0

RESEARCH ARTICLE

Monotonicity and nonmonotonicity in L₃-valued propositional logic

Wei LI¹, Yuefei SUI^2,³(

)

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

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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 $L 3$ -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.

Keywords sequent multisequent gentzen deduction system monotonicity nonmonotonicity

Corresponding Author(s): Yuefei SUI

Just Accepted Date: 16 March 2021 Issue Date: 15 November 2021

Cite this article:

Wei LI,Yuefei SUI. Monotonicity and nonmonotonicity in L₃-valued propositional logic[J]. Front. Comput. Sci., 2022, 16(4): 164315.

URL:

https://academic.hep.com.cn/fcs/EN/10.1007/s11704-021-0382-0
https://academic.hep.com.cn/fcs/EN/Y2022/V16/I4/164315

Fig.1

1	A Avron . Natural 3-valued logics-characterization and proof theory. The Journal of Symbolic Logic, 1991, 56( 1): 276– 294
2	A Avron . Gentzen-type systems, resolution and tableaux. Journal of Automated Reasoning, 1993, 10 : 265– 281
3	W Li , Y Sui . Multisequent Gentzen deduction systems for B22-valued first-order logic.. Articial Intelligence Research, 2018, 7( 1): 53– 62
4	M Baaz , C G Fermüller , G Salzer , R Zach . Labeled calculi and finite-valued logics. Studia Logica, 1998, 61 : 7– 33
5	Fitting M C. Many-valued modal logics. Fundamenta Informaticae, 1991, 15(3−4): 235−254
6	Zach R. Proof theory of finite-valued logics. Technical Report TUW-E185.2-Z.1-93, Institut Für Computersprachen, Technische Universität Wien, 1993
7	Malinowski G. Many-valued logic and its philosophy. In: Gabbay D M, Woods D J, eds. Handbook of the History of Logic, Vol.8. The Many Valued and Nonmonotonic Turn in Logic. Elsevier, 2009
8	E L Post . Determination of all closed systems of truth tables. Bulletin American Mathematical Society, 1920, 26 : 437–
9	Li W. Mathematical Logic, Foundations for Information Science. Progress in Computer Science and Applied Logic, vol.25. Birkhäuser, 2010

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