Affiliations: College of Computer Science, Shaanxi Normal University, Xi'an 710062, China. phyu76@126.com | Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, 200062, Shanghai, China. mzhang@sei.ecnu.edu.cn | Information Engineer College, Hangzhou Dianzi University, 310018, Hangzhou, China. wuhengy_1974@aliyun.com | Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, 200062, Shanghai, China. yxchen@sei.ecnu.edu.cn
Note: [] Address for correspondence: Shanghai Key Lab. of Trustworthy Comp., East China Normal Univ., 200062, Shanghai, China
Abstract: To model and analyze systems with multi-valued information, in this paper, we present an extension of Kripke structures in the framework of complete residuted lattices, which we will refer to as lattice-valued Kripke structures (LKSs). We then show how the traditional trace containment and equivalence relations, can be lifted to the lattice-valued setting, and we introduce two families of lattice-valued versions of the relations. Further, we explore some interesting properties of these relations. Finally, we provide logical characterizations of our relations by a natural extension of linear temporal logic.
