Data-Driven Statistical Learning of Temporal Logic Properties

TitleData-Driven Statistical Learning of Temporal Logic Properties
Publication TypeConference Paper
Year of Publication2014
AuthorsBartocci E, Bortolussi L, Sanguinetti G
Conference Name12th International Conference on Formal Modeling and Analysis of Timed Systems, {FORMATS} 2014.
SeriesLecture Notes in Computer Science
Conference LocationFirenze, Italy.

We present a novel approach to learn logical formulae characterising the emergent behaviour of a dynamical system from system observations. At a high level, the approach starts by devising a data-driven statistical abstraction of the system. We then propose general optimisation strategies for selecting formulae with high satisfaction probability, either within a discrete set of formulae of bounded complexity, or a parametric family of formulae. We illustrate and ap- ply the methodology on two real world case studies: characterising the dynamics of a biological circadian oscillator, and discriminating different types of cardiac malfunction from electro-cardiogram data. Our results demonstrate that this approach provides a statistically principled and generally usable tool to logically characterise dynamical systems in terms of temporal logic formulae.