Backward through Time, Algebraically

A new arXiv paper (2608.17087v1) introduces telos, a PyTorch library providing an algebra-generic, differentiable evaluation engine for linear temporal logic, enabling gradient-based training of softly-valued systems such as neural policies and adaptive controllers. The engine supports multiple semantic algebras, each representing a different choice of how to handle satisfaction and disappointment in both forward and backward passes, and is available at https://github.com/konstantinosKokos/telos.

arXiv:2608.17087v1 Announce Type: new Abstract: Linear temporal logic is a modal extension of propositional logic that allows one to state how a system should behave over time. Its canonical domain is the booleans, but discretely-valued judgements are of little use in steering softly-valued systems neural policies, adaptive controllers, sequence models, etc . In such cases, the goal formula's dis satisfaction becomes a training signal, and differentiability becomes a prime concern. Candidate differentiable semantics abound, but navigating them is tricky. Implementations, where available, are shallow embeddings, demanding an upfront commitment to a single semantic algebra and its usually implicit conduct. The paper casts the reader as a functional programmer asked to come to terms with this predicament, and refusing. Out of that refusal comes an evaluation engine that is algebra-generic and amenable to differentiation, together with an executable specification of the algebras it can accept. Various algebras are implemented and audited for their behavior, both forward and backward. Each algebra turns out to be a choice of which direction to disappoint, and how. Everything described and more is part of the PyTorch library telos, to be found at https://github.com/konstantinosKokos/telos.