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

Daham Mustafa; Diego Collarana; Sabrina Kirrane; Christoph Lange; Christoph Quix; Rafiqul Haque; Yixin Peng; Stefan Decker

cs.CLFeb 23, 2026

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

Authors: Daham Mustafa, Diego Collarana, Sabrina Kirrane, Christoph Lange, Christoph Quix, Rafiqul Haque, Yixin Peng, Stefan Decker

Organizations: RWTH Aachen University, Aachen, Germany · Fraunhofer FIT, Sankt Augustin, Germany · Vienna University of Economics and Business (WU), Vienna, Austria · University of Galway, Galway, Ireland

Abstract

The Open Digital Rights Language (ODRL) represents policy constraints as triples of a left operand, an operator, and a value. Several spatial operands, however, range over multi-axis domains such as width, height, and depth, while the constraint syntax provides no explicit axis identity. As a result, policy engines cannot determine whether multiple constraints apply to the same axis or different ones, making conflict detection unsound or incomplete. We resolve this ambiguity by axis decomposition, replacing multi-axis operands with axis-specific scalar operands over totally ordered domains. Each constraint then denotes an interval per axis and each policy an axis-aligned box, reducing conflict detection to box comparison. We define a three-valued semantics (Conflict, Compatible, Unknown), prove the decomposition sound and backward compatible with ODRL, instantiate it as ODRL Axis-Aligned Profile (OAAP), and validate it on a benchmark of 256 ODRL policy problems, each expressed in Turtle and compiled to first-order (TPTP) and SMT-LIB form, using Vampire, E, Z3, and cvc5.

Figures & tables

Operand class	Value space	Operands
Asset size	$\prod_{i=1}^{n}(0,\infty)$ , $n\in\{2,3\}$	absoluteSize , relativeSize
Asset position	$\prod_{i=1}^{n}[0,L_{i}]$ , $n\in\{2,3\}$	absoluteSpatialPosition , relativeSpatialPosition
Coordinates	$\mathbb{R}^{n}$ , $n\in\{2,3\}$	spatialCoordinates

Table 1: Dimensional ODRL left operands. Each value space is a product of totally ordered real-valued domains, one per axis.

L_{i}

denotes the extent of axis

i

ID	OAAP operand	Offer	Request	Verdict	Reason
$c_{1},c^{\prime}_{1}$	oaap:Width	$\textsf{lteq}\ 1920$	$\textsf{eq}\ 2400$	Conflict	$(0,1920]\cap\{2400\}=\emptyset$
$c_{2},c^{\prime}_{2}$	oaap:Height	$\textsf{lteq}\ 1080$	$\textsf{eq}\ 800$	Compatible	$800\in(0,1080]$
$c_{3}$	oaap:Depth	$\textsf{lteq}\ 50$	—	Unknown	No depth bound

Table 2: Per-axis constraints and verdicts for Example 1 . The offer (

c_{i}

, from provider BSB) and request (

c^{\prime}_{i}

, from consumer BnF) are decomposed under OAAP from odrl:absoluteSize into odax:absoluteSize{Width,Height,Depth} (abbreviated :Width , :Height , :Depth ). Verdicts follow Definitions 9 and 10 .

Base operand	Axis operand (IRI)	$D_{k}$
absoluteSize	oaap:absoluteSizeWidth	$(0,\infty)$
	oaap:absoluteSizeHeight	$(0,\infty)$
	oaap:absoluteSizeDepth	$(0,\infty)$
relativeSize	oaap:relativeSizeWidth	$(0,100]$
	oaap:relativeSizeHeight	$(0,100]$
	oaap:relativeSizeDepth	$(0,100]$

Table 3: The 15 axis-specific left operands of OAAP. Value domain

D_{k}

is fixed by the profile.

Group	$N$	Validates
Interval & box denotation	76	Per-axis intervals, 2D/3D boxes, projection, normalisation, well-formedness ( Definitions 5 , 7 , 3.2 , 2 and 4 )
Conflict criterion	32	Endpoint-precedence disjointness and open/closed boundary cases ( Theorems 3.1 and 6 )
Logical composition	45	and / or / xone verdict composition ( Definitions 14 , 15 and 4.2 )
Containment & completion	33	Box containment and Unknown completion sharpness ( Definitions 11 and 4.1 )
Runtime	10	Request satisfaction, permit/deny ( Definitions 17 and 4.4 )
Soundness (negative)	40	Deliberately wrong verdicts; each refutation witnesses soundness

Table 4: Benchmark groups, in the order the paper develops them.

N

is the problem count; every problem is verified by all four provers (E, Vampire, Z3, cvc5).

Policy Evaluation

Policy evaluation estimates the outcomes, value, risks, and fairness of decision rules before or after deployment.

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Feb 23, 2026J/K move · Enter open · S save

Denotational Semantics for ODRL: Knowledge-Based Constraint Conflict Detection

Daham Mustafa, Diego Collarana, Yixin Peng, Rafiqul Haque+3

RWTH Aachen University, Germany · Fraunhofer FIT, Sankt Augustin, Germany · University of Galway, Ireland

Policy Evaluation Knowledge Representation Constraint Satisfaction

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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.

Abstract

Policy Evaluation

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