A kernel function for Signal Temporal Logic formulae

TL;DR

This paper introduces a kernel function for Signal Temporal Logic (STL) formulae, enabling their embedding into a Hilbert space and facilitating kernel-based machine learning applications in temporal logic contexts.

Contribution

It proposes a novel kernel for STL formulae, allowing the use of kernel methods for learning and analysis in temporal logic spaces.

Findings

Kernel enables embedding STL formulae into Hilbert space

Application demonstrated in regression for probabilistic models

Facilitates machine learning in temporal logic domains

Abstract

We discuss how to define a kernel for Signal Temporal Logic (STL) formulae. Such a kernel allows us to embed the space of formulae into a Hilbert space, and opens up the use of kernel-based machine learning algorithms in the context of STL. We show an application of this idea to a regression problem in formula space for probabilistic models.