Abstract
Temporal logic provides designers a formal reasoning tool for specifying complex spatio-temporal behaviors and tasks for autonomous systems. Many techniques exist for control synthesis according to temporal logic specifications, spanning a large variety of systems, including robotics. However, the vast majority of implementations are limited to Boolean temporal logics. Boolean temporal logic does not have an innate mechanism for quantifying abstention, rather verdicts are either definitively \textit{True} or \textit{False}. Recent work demonstrates that ternary logic is a capable formalism for reasoning about robotic behaviors, with the natural ability to classify uncertainty with the \textit{Unknown} literal. Ternary temporal logic is still in its infancy, with work limited to synthesis for linear systems and monitoring. This work proposes a probabilistic relaxation of ternary temporal logic that allows for value and gradient computation through the same network while retaining exact verdicts on actual data. The relaxed network can be used as an objective in gradient-based control synthesis for both offline and online robotic control applications. We demonstrate the utility of our framework with two robotic manipulator tasks, one offline and one online, involving intermediate checking and sequencing of subtasks to demonstrate the benefit of our approach in terms of correct and timely execution.
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Publication details
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- Green open access
Cite this article
APA 7
Matheu, R., Damera, S. S., Baras, J. S., & Belta, C. (2026). Differentiable Ternary Temporal Logic Semantics with Polynomial Surrogate Networks. https://omanscience.com/en/articles/differentiable-ternary-temporal-logic-semantics-with-polynomial-surrogate-networks
MLA 9
Matheu, Ryan, et al. "Differentiable Ternary Temporal Logic Semantics with Polynomial Surrogate Networks." https://omanscience.com/en/articles/differentiable-ternary-temporal-logic-semantics-with-polynomial-surrogate-networks.
Chicago (author–date)
Matheu, Ryan, Sai Sandeep Damera, John S. Baras, and Calin Belta. 2026. "Differentiable Ternary Temporal Logic Semantics with Polynomial Surrogate Networks." https://omanscience.com/en/articles/differentiable-ternary-temporal-logic-semantics-with-polynomial-surrogate-networks.
Harvard
Matheu, R., Damera, S. S., Baras, J. S. and Belta, C. (2026) 'Differentiable Ternary Temporal Logic Semantics with Polynomial Surrogate Networks', Available at: https://omanscience.com/en/articles/differentiable-ternary-temporal-logic-semantics-with-polynomial-surrogate-networks.
Vancouver
Matheu R, Damera SS, Baras JS, Belta C. Differentiable Ternary Temporal Logic Semantics with Polynomial Surrogate Networks. https://omanscience.com/en/articles/differentiable-ternary-temporal-logic-semantics-with-polynomial-surrogate-networks
IEEE
R. Matheu, S. S. Damera, J. S. Baras, and C. Belta, "Differentiable Ternary Temporal Logic Semantics with Polynomial Surrogate Networks," https://omanscience.com/en/articles/differentiable-ternary-temporal-logic-semantics-with-polynomial-surrogate-networks.