On K-modal BL-logics

Article type: Research Article

Authors: Eslami, Esfandiar | Yousefi Kia, Omid | Borumand Saeid, Arsham^*

Affiliations: Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran

Correspondence: [*] Correspondence to: Dr. Arsham Borumand Saeid, Department of Pure Mathematics, Faculty of Mathematics and Computer Science, Shahid Bahonar University of Kerman, Kerman, Iran.Tel.: +98 34 31322490; Fax: +98 34 33201080; arsham@uk.ac.ir

Abstract: This article will introduce K-modal BL-logic and investigate some properties of this new logic. Consequently, T-modal BL-logic and S4-modal BL-logic, as schematic extensions of K-modal BL-logic, will be dealt with. Likewise, the algebraic semantics based on each logic will be constructed. Finally, the soundness and completeness theorems of these logics will be proved.

Keywords: (K-modal) T -modal BL-algebra, (K-modal) T -modal BL-logic

DOI: 10.3233/IFS-151604

Journal: Journal of Intelligent & Fuzzy Systems, vol. 29, no. 1, pp. 377-388, 2015