The B₄-valued propositional Belnap-Dunn logic¹

Article type: Research Article

Authors: Cungen, Cao^a | Bo, Chen^{a; b; *} | Yuefei, Sui^a

Affiliations: [a] Key Laboratory of Intelligent Information Processing, Institute of Computing Technology, Chinese Academy of Sciences, Beijing, China | [b] University of Chinese Academy of Sciences, Beijing, China

Correspondence: [*] Correspondence author: Chen Bo. Tel.: +86 15201305627; Fax: +86 10 62600509; E-mail: [email protected]

Note: [1] This work was supported by the National Natural Science Foundation of China (Grant No. 91224006, 61035004, 61173063, 61203284).

Abstract: A B4-valued propositional Belnap-Dunn logic will be proposed in this paper which there are two unary connectives [⊤] , [⊥] to represent the two middle values ⊤, ⊥ , respectively, and a Gentzen-typed deduction system will be given so that the system is sound and complete with the four-valued semantics of the propositional Belnap-Dunn logic.

Keywords: The Belnap-Dunn logic, unary connective, the soundness, the completeness

DOI: 10.3233/IFS-151548

Journal: Journal of Intelligent & Fuzzy Systems, vol. 28, no. 6, pp. 2705-2713, 2015