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Data-driven statistical learning of temporal logic properties. (English) Zbl 1448.68371

Legay, Axel (ed.) et al., Formal modeling and analysis of timed systems. 12th international conference, FORMATS 2014, Florence, Italy, September 8–10, 2014. Proceedings. Berlin: Springer. Lect. Notes Comput. Sci. 8711, 23-37 (2014).
Summary: 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 apply 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.
For the entire collection see [Zbl 1317.68012].

MSC:

68T05 Learning and adaptive systems in artificial intelligence
03B44 Temporal logic
62P10 Applications of statistics to biology and medical sciences; meta analysis
92C42 Systems biology, networks
93B15 Realizations from input-output data
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