arXiv subjects

Ryan Matheu

Publications and source records attributed to Ryan Matheu.

7 recordsLinked to original sources

arXiv2026

Contract-Based Agentic Systems Engineering: Delegation as Quotient for Assured System Design

A component an agent builds from a prompt can satisfy it and still break the system it joins, because the prompt omits what its neighbours assume of it. The artifact to hand over is computed, not written. A SysML v2 requirement with assumed and required constraints is an assume/guarantee contract, so when a system requirement is decomposed over fixed neighbours, the open component's requirement is the contract quotient, the weakest sound one, and again a SysML v2 requirement. Its required constraints carry the neighbours' assumptions, which a requirement for the mission alone drops and unit tests with mocked neighbours cannot reach. Signal Temporal Logic is closed under the quotient. We build the requirements, with derivation, allocation, satisfaction and verification, as a SysML~v2 model and compute the quotient from it. A case study delegates the local controller of a simulated warehouse robot, whose route crosses a worker's path and ends at a dock, to one language model under the quotient requirement, a mission-only requirement and a natural-language task, and scores the deliveries on live episodes against the system requirement from ground truth.

eess.SY↗

arXiv2026

SparseMax-dSTL: Sound Robustness with Horizon-Independent Gradient Allocation for Temporal Logic Trajectory Optimization

A gradient-based solver that enforces a Signal Temporal Logic (STL) specification uses a smooth approximation of its quantitative semantics, the robustness. In safety-critical trajectory optimization, this approximation must have two properties. First, it must be sound, that is, nonnegative only on trajectories that satisfy the specification. Second, at each temporal operator, the weight of its gradient on the violating samples must stay bounded away from zero, however long the horizon. The approximations in use, including the log-sum-exp, its sound variant, and the generalized-mean robustness, do not have both. We introduce lower approximations of the minimum and the maximum whose gradients are sparsemax projections, and we prove that the robustness built from them has both. It lies below the exact robustness and is therefore sound, and its error has a bound that is independent of the number of samples and known before optimization. The gradient of each approximation is exactly zero on every sample beyond a data-dependent threshold, so the weight on violating samples a gap beyond the others has a positive lower bound at every horizon. On a planar unicycle and on a seven-joint manipulator beside a person in simulation, the log-sum-exp approximation is positive on a violating trajectory. As the horizon of the manipulator's task grows from 10 to 80 s, the gradient weight of the sound variant on the violating samples falls from 0.22 to 0.04, while that of sparsemax stays at 1. In a constrained trajectory optimization of the unicycle, the constraint on the log-sum-exp robustness returns a violating trajectory, whereas the constraint on the sparsemax robustness returns a trajectory that satisfies the specification with the required margin.

eess.SY↗

arXiv2026

Ternary Logic Encodings of Temporal Behavior Trees with Application to Control Synthesis

Behavior Trees (BTs) provide designers with an intuitive graphical interface to construct long-horizon plans for autonomous systems. To ensure their correctness and safety, rigorous formal models and verification techniques are essential. Temporal BTs (TBTs) offer a promising approach by leveraging existing temporal logic formalisms to specify and verify the executions of BTs. However, this analysis is currently limited to offline post hoc analysis and trace repair. In this paper, we reformulate TBTs using a ternary-valued Signal Temporal Logic (STL) amenable to control synthesis. Ternary logic introduces a third truth value Unknown, formally capturing cases where a trajectory has neither fully satisfied nor violated a specification. We propose mixed-integer linear encodings for partial trajectory STL and TBTs over ternary logic, allowing for correct-by-construction control strategies for linear dynamical systems via mixed-integer optimization. We demonstrate the utility of our framework by solving optimal control problems.

cs.RO↗

arXiv2026

Differentiable Ternary Temporal Logic Semantics with Polynomial Surrogate Networks

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.

eess.SY↗

arXiv2026

IDDMBSE: Integrating Data-Driven and Model-Based Systems Engineering for Trusted Autonomous Cyber-Physical Systems

Autonomous cyber-physical systems (CPS) sit at the intersection of Model-Based Systems Engineering (MBSE) and data-driven Machine Learning and Artificial Intelligence (ML/AI), yet no integrated Systems Engineering (SE) methodology natively spans both. We address this gap with IDDMBSE, an Integrated Data-Driven and Model-Based Systems Engineering methodology that extends the rigorous MBSE V-process with a data-driven loop at every step, anchored in SysML, the autonomy stack, and a hybrid model-based plus data-driven trade-off architecture. We instantiate IDDMBSE as an interoperable, open-source tool chain: PERFECT, which maps SysML system architectures to executable ROS autonomy stacks for scalable performance evaluation; TRADES-X, which decomposes design-space exploration into a model-based optimization stage followed by a data-driven evaluation stage; and VERITAS, which combines formal, data-driven, and runtime verification into a single assurance workflow. We demonstrate IDDMBSE on a Trusted Autonomous Ground Robot across its development lifecycle, spanning sensor-suite selection, risk-sensitive path planning, behavior-tree task verification, conformal-prediction-based robust perception, and assured multi-robot coordination, all exercised in a contested-terrain Isaac Sim test range that we release with the tool chain. We close by sketching how IDDMBSE is being re-formulated on SysML v2 / KerML foundations to enable language-native composability and tighter ML/AI integration.

cs.RO↗

arXiv2026

On the Stability and Realizability of Recurrent Polynomial Surrogate Ternary Logic Gate Networks

Recurrent Neural Networks (RNNs) can learn to predict Signal Temporal Logic (STL) verdicts online from partial trajectories, but deploying them as runtime monitors in safety-critical systems demands more than predictive accuracy. Standard RNN architectures offer no structural guarantee that outputs degrade gracefully under sensor degradation; a dropped input can silently flip a verdict from safe to unsafe. We introduce the Recurrent Differentiable Ternary Logic Gate Network (R-DTLGN), a recurrent architecture that operates over Kleene's three-valued logic $\{-1, 0, +1\}$, where $0$ explicitly represents unknown. The R-DTLGN trains through continuous polynomial surrogates and hardens to a discrete ternary logic circuit at inference. We analyze the hardened circuit through two gate vocabularies derived from two orderings on the ternary domain: numerically monotone gates ensure stable recurrent dynamics, while information-monotone gates, when present, guarantee principled abstention (unknown inputs never produce wrong outputs) and monotonicity in input certainty (more information can only improve the verdict). We show that the recurrent connections required by bounded STL operators use exclusively AND and OR, which belong to both vocabularies, linking the monitoring task to the architecture's guarantees. A realizability bound derived from the STL formula's temporal operators directly sizes the network's hidden state, replacing hyperparameter search with a formula-driven specification. We evaluate on STL specifications over D4RL PointMaze navigation data, testing prediction accuracy, degradation under predicate dropout, and the accuracy-versus-safety tradeoff between two label construction pipelines. The R-DTLGN is, to our knowledge, the first recurrent architecture that couples learned temporal prediction with formal degradation guarantees rooted in three-valued logic.

cs.LG↗

arXiv2026

Polynomial Surrogate Training for Differentiable Ternary Logic Gate Networks

Differentiable logic gate networks (DLGNs) learn compact, interpretable Boolean circuits via gradient-based training, but all existing variants are restricted to the 16 two-input binary gates. Extending DLGNs to Ternary Kleene $K_3$ logic and training DTLGNs where the UNKNOWN state enables principled abstention under uncertainty is desirable. However, the support set of potential gates per neuron explodes to $19{,}683$, making the established softmax-over-gates training approach intractable. We introduce Polynomial Surrogate Training (PST), which represents each ternary neuron as a degree-$(2,2)$ polynomial with 9 learnable coefficients (a $2{,}187\times$ parameter reduction) and prove that the gap between the trained network and its discretized logic circuit is bounded by a data-independent commitment loss that vanishes at convergence. Scaling experiments from 48K to 512K neurons on CIFAR-10 demonstrate that this hardening gap contracts with overparameterization. Ternary networks train $2$-$3\times$ faster than binary DLGNs and discover true ternary gates that are functionally diverse. On synthetic and tabular tasks we find that the UNKNOWN output acts as a Bayes-optimal uncertainty proxy, enabling selective prediction in which ternary circuits surpass binary accuracy once low-confidence predictions are filtered. More broadly, PST establishes a general polynomial-surrogate methodology whose parameterization cost grows only quadratically with logic valence, opening the door to many-valued differentiable logic.

cs.LG↗