Formally Verified Neurosymbolic Trajectory Learning via Tensor-based Linear Temporal Logic on Finite Traces
This provides a rigorous framework for constrained training in neurosymbolic systems, addressing safety and correctness issues for researchers and practitioners in formal methods and machine learning integration.
The authors developed a formally verified neurosymbolic learning framework that integrates tensor semantics for linear temporal logic on finite traces (LTLf) with theorem prover Isabelle/HOL, creating a differentiable loss function that enables training to satisfy logical constraints while eliminating risks of manual implementations in unsafe languages like Python.
We present a novel formalisation of tensor semantics for linear temporal logic on finite traces (LTLf), with formal proofs of correctness carried out in the theorem prover Isabelle/HOL. We demonstrate that this formalisation can be integrated into a neurosymbolic learning process by defining and verifying a differentiable loss function for the LTLf constraints, and automatically generating an implementation that integrates with PyTorch. We show that, by using this loss, the process learns to satisfy pre-specified logical constraints. Our approach offers a fully rigorous framework for constrained training, eliminating many of the inherent risks of ad-hoc, manual implementations of logical aspects directly in an "unsafe" programming language such as Python, while retaining efficiency in implementation.