Time series checking with fuzzy interval temporal logics

Model checking is a very well-known problem, with many practical applications. A possible variation of such a problem in the interval logic setting is the so-called finite model checking, that consists of verifying an interval temporal logic formula, typically of Halpern and Shoham's logic of Allen's relations HS, on a fully represented finite interval model. Multivariate time series are collections of temporally ordered sets of values, and they allow to describe a variety of situations, such as the medical history of an hospitalized patient or the sensor values during a plane flight. In this paper we argue how the recently introduced fuzzy generalization of interval temporal logic is a suitable language in which interesting properties of a multivariate time series can be expressed and checked, and we define, solve, and discuss the complexity of the multivariate time series fuzzy interval logic checking problem.