Fuzzy Halpern and Shoham's interval temporal logics - Conradie, Willem; Della Monica, Dario; Muñoz-Velasco, Emilio José; Sciavicco, Guido; Stan, Ionel Eduard (Elsevier, 2023)
The most representative interval temporal logic, called HS, was introduced by Halpern and Shoham in the nineties. Recently, HS has been proposed as a suitable formalism for modern artificial intelligence applications; however, when dealing with real-life data one is not always able to express temporal relations and propositional labels in a definite, crisp way. In this paper, following the seminal ideas of Fitting and Zadeh, we present a fuzzy generalization of HS, called FHS, that partially solves such problems of expressive power. We study FHS from both a theoretical and an application standpoint: first, we discuss its syntax, semantics, expressive power, and satisfiability problem; then, we define and solve the time series FHS finite model checking problem, to serve as the basis of future applications.
Keywords: Modalidad (Lógica); Fuzzy interval temporal logic; Satisfiability; Expressive power; Finite model checking; Decidability