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.
Fuzzy Halpern and Shoham's interval temporal logics / Conradie, Willem; Della Monica, Dario; Muñoz-Velasco, Emilio; Sciavicco, Guido; Stan, Ionel Eduard. - In: FUZZY SETS AND SYSTEMS. - ISSN 0165-0114. - 456:(2023), pp. 107-124. [10.1016/j.fss.2022.05.014]
Fuzzy Halpern and Shoham's interval temporal logics
Sciavicco, Guido;Stan, Ionel Eduard
2023-01-01
Abstract
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.File | Dimensione | Formato | |
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