Axis Decomposition for ODRL: Resolving Dimensional Ambiguity in Policy Constraints through Interval Semantics

2026-02-23

AI Summary

This work addresses the axial ambiguity inherent in multidimensional operands under single-scalar constraints in ODRL 2.2, which leads to non-deterministic policy evaluation. To resolve this, the authors propose an axis-decomposition framework that refines multidimensional operands into axis-specific scalar operands, enabling deterministic interpretation and conflict detection through interval semantics. The approach guarantees deterministic semantics, AABB completeness, sound over-approximation under projection, and conservative extensibility, supporting three-valued logic for conflict resolution. The meta-theory is formally verified in Isabelle/HOL, and policy validation is implemented via integration with TPTP (Vampire) and SMT-LIB (Z3) solvers. Evaluation across 117 benchmark problems spanning nine scenario categories demonstrates complete solver agreement, and the method has been successfully deployed in real-world applications such as cultural heritage data spaces.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Knowledge Representation and Reasoning: Description Logics
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty

Application Category

• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Semantics and Knowledge: Provenance, trust, security and privacy, and ethical issues in managing semantic data
• Security and Privacy: Data transparency and provenance

Abstract

Every ODRL 2.2 constraint compares a single scalar value: (leftOperand, operator, rightOperand). Five of ODRL's approximately 34 left operands, however, denote multi-dimensional quantities--image dimensions, canvas positions, geographic coordinates--whose specification text explicitly references multiple axes. For these operands, a single scalar constraint admits one interpretation per axis, making policy evaluation non-deterministic. We classify ODRL's left operands by value-domain structure (scalar, dimensional, concept-valued), grounded in the ODRL 2.2 specification text, and show that dimensional ambiguity is intrinsic to the constraint syntax. We present an axis-decomposition framework that refines each dimensional operand into axis-specific scalar operands and prove four properties: deterministic interpretation, AABB completeness, sound over-approximation under projection, and conservative extension. Conflict detection operates in two layers: per-axis verdicts are always decidable; box-level verdicts compose through Strong Kleene conjunction into a three-valued logic (Conflict, Compatible, Unknown). For ODRL's disjunctive (odrl:or) and exclusive-or (odrl:xone) logical constraints, where per-axis decomposition does not apply, the framework encodes coupled multi-axis conjectures directly. We instantiate the framework as the ODRL Spatial Axis Profile--15 axis-specific left operands for the five affected base terms--and evaluate it on 117 benchmark problems spanning nine categories across both TPTP FOF (Vampire) and SMT-LIB (Z3) encodings, achieving full concordance between provers. Benchmark scenarios are inspired by constraints arising in cultural heritage dataspaces such as Datenraum Kultur. All meta-theorems are mechanically verified in Isabelle/HOL.

Problem

• ODRL
• dimensional ambiguity
• policy constraints
• axis decomposition
• interval semantics

Innovation

• axis decomposition
• dimensional ambiguity
• interval semantics
• ODRL policy constraints
• formal verification