Formally Verified Neurosymbolic Trajectory Learning via Tensor-based Linear Temporal Logic on Finite Traces

• URL: http://arxiv.org/abs/2501.13712v1
• Date: Thu, 23 Jan 2025 14:43:12 GMT
• Title: Formally Verified Neurosymbolic Trajectory Learning via Tensor-based Linear Temporal Logic on Finite Traces
• Authors: Mark Chevallier, Filip Smola, Richard Schmoetten, Jacques D. Fleuriot,
• Abstract summary: We present a novel formalisation of tensor semantics for linear temporal logic on finite traces (LTLf) We demonstrate that this formalisation can be integrated into a neurosymbolic learning process by defining and verifying a differentiable loss function for the constraints. We show that, by using this loss, the process learns to satisfy pre-specified logical constraints.
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• Abstract: 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.

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