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.

翻译：ODRL的六个基于集合的运算符——isA、isPartOf、hasPart、isAnyOf、isAllOf、isNoneOf——依赖于W3C规范未明确指定的外部领域知识。若缺乏该知识，所有跨数据空间策略比较均默认结果为Unknown。本文提出一种指称语义，将每个ODRL约束映射到满足该约束的知识库概念集合。冲突检测可归结为在三值判定（Conflict、Compatible或Unknown）下的指称交集运算，该判定在不完备知识下具有可靠性。本框架涵盖ODRL全部三种组合模式（and、or、xone）以及实践中出现的全部三种语义域：分类学域（类包含关系）、部分整体域（部分-整体包含关系）和指称域（同一性关系）。针对跨数据空间互操作性，我们定义了知识库间保持序关系的对齐映射，并证明了两项保证：冲突在不同知识库标准间得以保持；未映射概念可优雅降级为Unknown——而绝不会产生虚假冲突。运行时可靠性定理确保设计阶段的判定在所有执行上下文中均成立。该形式化编码保持在可判定的一阶逻辑EPR片段内。我们通过154个基准测试在六个知识库体系（GeoNames、ISO 3166、W3C DPV、GDPR衍生分类体系、BCP 47及ISO 639-3）和四个针对对抗性边缘案例的结构化知识库上进行验证，Vampire定理证明器与Z3 SMT求解器对所有154项判定结果均达成一致。关键发现表明：互斥组合（xone）需要比合取或析取更严格的知识库公理——即使在正面证据看似恰好满足单分支的情况下，开放世界语义仍会阻碍互斥性的成立。