Conflict-Free Policy Languages for Probabilistic ML Predicates: A Framework and Case Study with the Semantic Router DSL

2026-03-18

AI Summary

Existing policy languages struggle to detect conflicts arising from threshold overlaps among rules based on probabilistic machine learning signals—such as embedding similarity—which can lead to erroneous routing or access control decisions. This work proposes a three-tier decidability framework that replaces independent thresholds with temperature-scaled Softmax, partitioning the embedding space into mutually exclusive Voronoi regions to fundamentally prevent concurrent rule triggering without requiring model retraining. We present the first systematic characterization of the decidability hierarchy for policy conflicts under probabilistic ML predicates and implement an efficient conflict detection and prevention mechanism within the Semantic Router domain-specific language. The approach has been successfully applied to LLM inference routing and is extensible to semantic role-based access control (RBAC) and API gateway policies.

Technology Category

• Planning, Routing, and Scheduling: Planning with Language Models
• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Probabilistic Circuits and Graphical Models

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

Conflict detection in policy languages is a solved problem -- as long as every rule condition is a crisp Boolean predicate. BDDs, SMT solvers, and NetKAT all exploit that assumption. But a growing class of routing and access-control systems base their decisions on probabilistic ML signals: embedding similarities, domain classifiers, complexity estimators. Two such signals, declared over categories the author intended to be disjoint, can both clear their thresholds on the same query and silently route it to the wrong model. Nothing in the compiler warns about this. We characterize the problem as a three-level decidability hierarchy -- crisp conflicts are decidable via SAT, embedding conflicts reduce to spherical cap intersection, and classifier conflicts are undecidable without distributional knowledge -- and show that for the embedding case, which dominates in practice, replacing independent thresholding with a temperature-scaled softmax partitions the embedding space into Voronoi regions where co-firing is impossible. No model retraining is needed. We implement the detection and prevention mechanisms in the Semantic Router DSL, a production routing language for LLM inference, and discuss how the same ideas apply to semantic RBAC and API gateway policy.

Problem

• conflict detection
• probabilistic ML predicates
• policy languages
• embedding conflicts
• semantic routing

Innovation

• probabilistic ML predicates
• conflict-free policy languages
• embedding space partitioning
• temperature-scaled softmax
• Voronoi regions