Abstract
The analysis of temporal series—in particular, analysis of multisensor data—is a complex problem. It depends on the application domain, the way the data have to be used, and sensors available, among other factors. Various models, algorithms, and technologies have been designed for this goal. Temporal logics are used to describe temporal properties of systems. The properties may specify the occurrence and the order of events in time, recurring patterns, complex behaviors, and processes. In this paper, a new interval logic, called duration calculus for functions (DC4F), is proposed for the specification of temporal series corresponding to multisensor data. DC4F is a natural extension of the well-known duration calculus, an interval temporal logic for the specification of process duration. The adequacy of the proposed logic is analyzed in the case of multisensor data concerning volcanic eruption monitoring. It turns out that the relevant behavior concerns time intervals, not only accumulated history as it is described in other kinds of temporal logics. The examples analyzed demonstrate that a description language is required to specify time series of various kind relative to time intervals. The duration calculus cannot be successfully applied for this task. The proposed calculus allows one to specify temporal series and complex interval-dependent behaviors, and to evaluate the corresponding data within a unifying logical framework. It allows to formulate hypotheses concerning volcano eruption phenomena. However, the expressivity of DC4F comes at the cost of its decidability.
Highlights
We show the basic properties of duration calculus (DC) in its original form
We present examples that are specific to DC4F and, cannot be expressed in Duration calculus (DC)
To demonstrate the applicability of DC4F, we looked at several examples of signal processing and the corresponding temporal series
Summary
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. Duration calculus (DC) is an interval logic that is widely used for the specifying, modeling, and reasoning about discrete and continuous processes It allows to specify propositional functions with Boolean values changing over time. It turns out that such phenomena and their dependencies may be conveniently specified using DC4F, as it provides a expressive and uniform language for expressing various phenomena in a precise way, models for various data, and evaluation and reasoning capabilities. DC4F, like DC, is an expressive language and is, undecidable, i.e., there is no general algorithm for deciding the question mentioned above This does not hinder its use for specification, nor does it hinder the validation of formulas for concrete data. The paper contains an Appendix in which we define the formal semantics of DC4F
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