Differentiable Inference of Temporal Logic Formulas
This work addresses the challenge of formalizing expert knowledge in legacy systems for better understanding and design improvement, representing a novel method for a known bottleneck in temporal logic inference.
The paper tackles the problem of learning Signal Temporal Logic formulas from system outputs by proposing the first Recurrent Neural Network architecture that infers formula structure via gradient descent, eliminating the need for predefined templates. It achieves similar or better mis-classification rates (MCR) than enumerative and lattice methods, with empirical results showing that different formulas can yield similar MCR, highlighting the under-determinism of the inference problem.
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 under-determinism of the problem of temporal logic inference.