Differentiable Inference of Temporal Logic Formulas

Abstract

We demonstrate the first Recurrent Neural Network architecture for learning Signal Temporal Logic formulas, and present the first systematic comparison of formula inference methods. Legacy systems embed much expert knowledge which is not explicitly formalized. There is great interest in learning formal specifications that characterize the ideal behavior of such systems -that is, formulas in temporal logic that are satisfied by the system's output signals. Such specifications can be used to better understand the system's behavior and improve design of its next iteration. Previous inference methods either assumed certain formula templates, or did a heuristic enumeration of all possible templates. This work proposes a neural network architecture that infers the formula structure via gradient descent, eliminating the need for imposing any specific templates. It combines learning of formula structure and parameters in one optimization. Through systematic comparison, we demonstrate that this method achieves similar or better mis-classification rates (MCR) than enumerative and lattice methods. We also observe that different formulas can achieve similar MCR, empirically demonstrating the underdeterminism of the problem of temporal logic inference.

Classification of Driving Behaviors Using STL Formulas: A Comparative Study

“…Incorporating preferences and priorities with temporal logics is studied in [1], [12], [30]- [32]. The work in [12] introduces a weighted variant of the STL, called Weighted Signal Temporal Logic (WSTL), in which weights reflect the order of priorities or preferences.…”

“…For the end-user, it is hard to interpret the weights and define their preferences in the temporal logic formalism, so there needs to be an intermediate step to infer the weights from the user. In [31], [32], a parametric extension of WSTL, which we call PWSTL, is used in a time series classification problem, where weights of the formula are learned using neural networks.…”

Policy Learning with Constraints in Model-free Reinforcement Learning: A Survey

“…In recent years, researchers have focused on inferring or mining STL specifications from data, to facilitate the development of safe and robust systems. A key approach to mining STL from data is the use of algorithmic techniques, such as optimization-based algorithms (Abbas et al 2014) and machine learning methods (Fronda and Abbas 2022). Optimization-based techniques seek to minimize an objective function that captures the distance between the candidate STL formulas and the given data traces.…”