Residuated Algebraic Structures in the Vicinity of Pre-rough Algebra and Decidability

Article type: Research Article

Authors: Lin, Zhe^a | Chakraborty, Mihir Kumar^b | Ma, Minghui^{c; *}

Affiliations: [a] Department of Philosophy, Xiamen University, Xiamen, China. pennyshaq@163.com | [b] Visiting Professor, School of Cognitive Science, Jadavpur University, Kolkata, India. mihirc4@gmail.com | [c] Department of Philosophy, Sun Yat-sen University, Guangzhou, China. mamh6@mail.sysu.edu.cn

Correspondence: [*] Address for correspondence: No. 135, Xingang Xi Road, Sun Yat-sen University, Guangzhou, China.

Abstract: Varieties of topological quasi-Boolean algebras in the vicinity of pre-rough algebras [28, 29] are expanded to residuated algebraic structures by introducing a new implication operation and its residual in these structures. Sequent calculi for some classes of residuated algebraic structures are established. These sequent calculi have the strong finite model property which yields the decidability of the word problem for corresponding classes of algebraic structures.

Keywords: Pre-rough algebra, residuation, word problem, finite model property, decidability

DOI: 10.3233/FI-2021-2023

Journal: Fundamenta Informaticae, vol. 179, no. 3, pp. 239-274, 2021