R-DTLGN: Recurrent Ternary Logic Networks for Stable STL Monitoring
The Recurrent Differentiable Ternary Logic Gate Network (R-DTLGN) introduces a novel recurrent neural network design aimed at predicting Signal Temporal Logic (STL) outcomes from incomplete trajectories. In contrast to traditional RNNs, R-DTLGN utilizes Kleene's three-valued logic {-1, 0, +1}, where 0 signifies an unknown state, thereby offering structural protections against unexpected verdict changes due to sensor failures. The training process employs continuous polynomial surrogates, transitioning to a discrete ternary logic circuit during inference. Two types of gate vocabularies are examined: numerically monotone gates promote stable recurrent behavior, while information-monotone gates enhance information retention. This research focuses on safety-critical runtime monitoring by facilitating gradual output degradation.
Key facts
- R-DTLGN operates over Kleene's three-valued logic {-1, 0, +1}
- 0 explicitly represents unknown in the logic
- Network trains through continuous polynomial surrogates
- Hardens to a discrete ternary logic circuit at inference
- Two gate vocabularies: numerically monotone and information-monotone
- Numerically monotone gates ensure stable recurrent dynamics
- Information-monotone gates optimize information preservation
- Addresses safety-critical runtime monitoring for sensor degradation
Entities
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