Axis-Aligned Semantics for ODRL: Resolving Dimensional Ambiguity in Policy Constraints

ODRL's six set-based operators -- isA, isPartOf, hasPart, isAnyOf, isAllOf, isNoneOf -- depend on external domain knowledge that the W3C specification leaves unspecified. Without it, every cross-dataspace policy comparison defaults to Unknown. We present a denotational semantics that maps each ODRL constraint to the set of knowledge-base concepts satisfying it. Conflict detection reduces to denotation intersection under a three-valued verdict -- Conflict, Compatible, or Unknown -- that is sound under incomplete knowledge. The framework covers all three ODRL composition modes (and, or, xone) and all three semantic domains arising in practice: taxonomic (class subsumption), mereological (part-whole containment), and nominal (identity). For cross-dataspace interoperability, we define order-preserving alignments between knowledge bases and prove two guarantees: conflicts are preserved across different KB standards, and unmapped concepts degrade gracefully to Unknown -- never to false conflicts. A runtime soundness theorem ensures that design-time verdicts hold for all execution contexts. The encoding stays within the decidable EPR fragment of first-order logic. We validate it with 154 benchmarks across six knowledge base families (GeoNames, ISO 3166, W3C DPV, a GDPR-derived taxonomy, BCP 47, and ISO 639-3) and four structural KBs targeting adversarial edge cases. Both the Vampire theorem prover and the Z3 SMT solver agree on all 154 verdicts. A key finding is that exclusive composition (xone) requires strictly stronger KB axioms than conjunction or disjunction: open-world semantics blocks exclusivity even when positive evidence appears to satisfy exactly one branch.

The ODRL language has become the standard for representing policies and regulations for digital rights. However its complexity is a barrier to its usage, which has caused many related theoretical and practical works to focus on different, and not interoperable, fragments of ODRL. Moreover, semantically equivalent policies can be expressed in numerous different ways, which makes comparing them and processing them harder. Building on top of a recently defined semantics, we tackle these problems by proposing an approach that involves a parametrised normalisation of ODRL policies into its minimal components which reformulates policies with permissions and prohibitions into policies with permissions exclusively, and simplifies complex logic constraints into simple ones. We provide algorithms to compute a normal form for ODRL policies and simplifying numerical and symbolic constraints. We prove that these algorithms preserve the semantics of policies, and analyse the size complexity of the result, which is exponential on the number of attributes and linear on the number of unique values for these attributes. We show how this makes complex policies representable in more basic fragments of ODRL, and how it reduces the problem of policy comparison to the simpler problem of checking if two rules are identical.

The ODRL policy language is emerging as the de-facto standard for policy modelling data access and usage preferences, AI governance policies and data workflows in European dataspaces. The current standard has no mathematical formal semantics to describe how a system should implement policy evaluation. This has resulted in a variety of systems and tools that implement their own interpretation of the language, which limits interoperability and cannot guarantee consistent results. Based on an existing semantic model of ODRL, we formalise the problems of ODRL evaluation for the access control and monitoring scenarios, in both static and streaming settings, and we provide a novel, efficient algorithm and implementation. We present the first ODRL Evaluator with transparent formal semantics and supporting all rule types. We experimentally measure its performance, analysing different scalability dimensions related to policy complexity and size of the data on which a policy is evaluated. We compare our system with the state-of-the-art by providing a comparative review of existing ODRL evaluators, which highlights the differences in supported ODRL features and evaluation modes.