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

Abstract

Every ODRL 2.2 constraint compares a single scalar value: (leftOperand, operator, rightOperand). Five of ODRL's 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, projection soundness, 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.