We present the Temporal Indirection Ontology Design Pattern, which models persistent identifiers whose referents evolve over time according to deterministic rules. The pattern introduces core abstractions that separate identifier persistence from time-dependent referent dynamics, enabling both stable referencing and precise historical reconstruction. This approach addresses a significant gap in existing temporal ontologies, which typically assume static identifier-referent relationships and therefore cannot capture scenarios where meaning evolves but referential continuity must be preserved. We validate the pattern through implementations in financial derivatives (e.g., generic identifiers such as “CL1” for front-month oil futures) and air transportation (flight numbers with daily-changing assignments). Our contributions include: (i) a reusable pattern grounded in foundational ontology concepts, (ii) competency question coverage demonstrating support for resolution, audit, and analysis tasks, and (iii) cross-domain evidence of applicability.
Many information systems rely on identifiers that remain stable while the entities they reference change systematically over time. This creates a fundamental challenge for knowledge representation: how can we preserve referential stability while accurately tracking what an identifier denotes at any given moment? Humans readily understand expressions like “the current president” or “the department head” as stable references to roles whose occupants change. Capturing this logic in an ontology, however, requires explicit modeling. We call this phenomenon temporal indirection—a situation where a persistent identifier maintains constant identity while the referent changes systematically according to deterministic rules.
Consider financial markets, where generic trading symbols like “CL1” serve as persistent identifiers for front-month crude oil futures contracts. This identifier provides a paradigmatic example of temporal indirection within financial information systems. A persistent identifier (CL1) serves as a stable referent while dynamically resolving to the front-month crude oil futures contract, thereby ensuring continuity across successive monthly contract rollovers. In January 2025, “CL1” refers to the February 2025 contract; when that contract approaches expiration, “CL1” automatically transitions to reference the March 2025 contract. Real-time market attributes—such as last trade price, trading volume, and settlement values—are bound to the current contract instance but exposed through the invariant identifier.
central to data ontology and financial knowledge representation. Operational implementations of this mechanism can be observed in public systems such as MarketWatch and TradingView, each of which provides continuous charting and contract metadata under the “CL1” identifier despite the underlying contract substitutions.
This pattern extends far beyond finance. Table 1 shows representative domains where temporal indirection proves essential. Air transportation employs stable flight numbers (e.g., “UA001”) that map 16th Workshop on Ontology Design and Patterns (WOP 2025) at ISWC, November 02–06, 2025, Nara, Japan " ysvetashova@bloomberg.net (Y. Svetashova) ~ https://github.com/YuliaS (Y. Svetashova) 0000-0003-1807-107X (Y. Svetashova)
© 2025 Copyright for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0). to diferent aircraft and crews daily. Healthcare systems track roles like “primary oncologist on duty” that persist while individual physicians rotate through shifts. In each case, the identifier provides continuity for reporting and analysis, while precise resolution determines the actual entity at any point in time.
Healthcare Environmental
Digital
Services Regulatory Primary Oncologist
Ward 7 River Station 1
Primary Payment API Latest Current GDPR
Individual physicians Physical sensors Implementation
versions
Specific rulings
1.1. Limitations of Current Approaches
Existing temporal ontologies fail to capture this indirection pattern adequately. Standard approaches
like PROV-O [
• A formal separation between persistent identifiers and their time-dependent referents, • Explicit representation of transition rules and resolution contexts, • Support for dual attribution (observations linked to both identifier and specific referent), • Complete audit trails of all referent transitions. 1.3. Paper Organization The remainder of this paper is structured as follows. Section 2 presents the Temporal Indirection Pattern’s abstract structure, beginning with core concepts and progressing through relationships, constraints, and competency questions. Section 3 demonstrates the pattern’s application to financial derivatives, showing how abstract classes map to domain concepts. Section 4 validates the pattern through comprehensive testing in both finance and aviation domains. Section 5 positions our contribution relative to existing temporal modeling approaches. Finally, Section 6 discusses implications and future directions.
This section presents the Temporal Indirection Ontology Design Pattern as a reusable solution for modeling persistent identifiers with evolving referents. We begin with the pattern’s conceptual foundations, then detail its structure, constraints, and validation criteria.
Stable Level Identifier remains constant over time Dynamic Level Referents change according to rules 1 1 Time (1) 2 2 Current 4 4 5 5 2.1. Conceptual Foundations The pattern addresses four fundamental requirements that emerge from temporal indirection scenarios:
their referents.
unambiguous.
2.2. Core Components The pattern can be used independently or aligned with foundational ontologies. It comprises seven core classes, each serving a specific role in the temporal indirection mechanism. Figure 2 illustrates their relationships.
A Persistent Identifier represents a stable reference that maintains consistent semantics for external systems. It exists independently of any particular referent and persists even during transition periods.
Oncologist, Ward 7”). When aligned with foundational ontologies, a persistent reference can be
considered an information object (e.g., dul:InformationObject1 in the DOLCE+DnS Ultralite (DUL) [
A Referent Entity is the actual entity that fulfills the persistent identifier at a given time. These entities have independent lifecycles: they exist before becoming associated with an identifier and continue after the association ends. In our financial example, specific futures contracts (e.g., “CLU25” for January 2025 delivery) serve as referent entities. In foundational ontology terms, these align with general entity concepts (e.g., dul:Entity).
: <http://ontologydesignpatterns.org/cp/owl/temporalindirection.owl#>, fd: <http://example.org/financial-derivatives#>, avo: <http://example.org/aviation-operations#>.
Standard prefixes ( rdf:, rdfs:, owl:, xsd:, dul:) follow conventions as documented at https://prefix.cc/.
• Precise temporal boundaries through start and end times • Tracking of transition events that initiate and terminate the binding • Validation of temporal integrity (no gaps or overlaps)
temporal interval2. Conceptually, it is a situation or context (cf. dul:Situation).
• The outgoing referent (via :changesFrom) • The incoming referent (via :changesTo) • The precise timestamp of transition • The rule that triggered the change (via :triggeredBy)
markets, these might specify “roll to next month’s contract on the 20th business day.” In aviation, they might state “assign next available aircraft 2 hours before scheduled departure.”
The Resolution Context provides the interpretive framework for determining active referents. It specifies which conventions apply, which rules are active, and how exceptions are handled. This concept parallels descriptive or normative elements in foundational ontologies (e.g., dul:Description) but functions independently as a rule specification.
include exchange trading calendars, hospital shift schedules, or software deployment policies.
Observations about entities require special handling to maintain both referential stability and specific attribution. An observation is linked to: 1) the persistent reference via :observedEntity (for continuity), 2) the specific referent entity that was active at observation time via :observedReferentEntity (for attribution), 3) observable properties that may apply to either the reference or the referent, 4) results that must be contextualized by both levels of indirection. This dual attribution enables queries that aggregate observations across all referents of a persistent reference while maintaining traceability to specific entities. 2.3. Structural Constraints
resolution context. This prevents the creation of orphaned identifiers.
interval. This ensures unambiguous resolution.
Traceability: Every transition event must specify both source and target referents, along with the triggering rule. This enables complete audit trails. 2In our implementation, we did not explicitly reuse time:Interval or related properties from OWL-Time. Instead, we introduced a custom :TemporalInterval class with :hasStartTime and :hasEndTime. In future iterations, we may consider aligning with OWL-Time by reusing time:hasBeginning/time:hasEnd for intervals and time:Instant for event timestamps, to leverage existing standards and improve interoperability. dul:TimeInterval dul:Quality dul:Norm 2.4. Competency Questions
CQ2 CQ3 CQ4 CQ5 CQ6 CQ7 CQ8
CQ1 Current Resolution
Which entity does a persistent identifier currently reference? Historical Resolution Which entity was referenced at a past timestamp? Transition Timing When did referent transitions occur? Attribution What observations are associated with specific referents? Complete History What is the full sequence of referents over time? Rule Provenance Which rules triggered specific transitions? Temporal Integrity Are there gaps or overlaps in temporal bindings? Context Reconstruction Can complete context be rebuilt for any time point?
3.1. Domain Context In commodity futures markets, traders rely on standardized symbols known as tickers to identify contracts. These generic identifiers, such as “CL1” for the front-month crude oil contract, allow traders to reference rolling positions without specifying which particular delivery month currently holds that designation. This enables continuous market analysis: traders can chart “CL1” prices over years without manually switching between individual contracts as they expire.
3.2. Pattern Specialization • fd:GenericTicker ⊑ :PersistentReference — stable market symbols • fd:FuturesContract ⊑ :ReferentEntity — specific dated contracts • fd:ContractMapping ⊑ :TemporalBinding — active ticker-contract relationships • fd:ContractRoll ⊑ :TransitionEvent — monthly roll events • fd:RollSchedule ⊑ :ResolutionContext — exchange-specific rules
This one-to-one mapping ensures, domain experts can understand the model while preserving the pattern’s temporal reasoning capabilities. 3.3. Domain Extensions
modifying pattern semantics.
temporal indirection behavior from constituent tickers.
Specialized Properties: fd:rollsFrom and fd:rollsTo extend the generic :changes property to express contract succession explicitly.
This section validates the Temporal Indirection Pattern through implementation and testing in two domains: financial derivatives and air transportation. We demonstrate query execution, measure competency question coverage, and analyze cross-domain applicability in a dedicated GitHub project at https://github.com/YuliaS/temporal_indirection.git. 4.1. Validation Methodology Our validation approach comprises: 1. Reference Implementation: Open-source repository [6] with pattern definition, domain ontologies, and test data 2. Competency Questions: SPARQL queries for all competency questions in each domain 3. Data Coverage: Three-month temporal spans of instance data • All datasets used in this validation were synthetically generated to avoid reliance on proprietary or copyrighted materials. We specified initial value ranges (e.g., plausible price intervals for futures contracts, typical aircraft capacities, and operational time windows) and provided descriptive metadata to guide generation. • Instance data was then produced automatically by applying domain-inspired rules and randomized sampling within these ranges. Specific identifiers were fabricated to resemble real-world formats while remaining entirely artificial. This approach ensured that the validation environment reflected realistic conditions while maintaining full compliance with copyright and licensing requirements.
and consistency
ontologies and synthetic datasets, executes the SPARQL competency-question suite, and performs integrity checks using small test harnesses over an in-memory RDFLib graph. Experiments were run with CPython 3.11 (Linux, x86_64) and RDFLib 7.0.0; SPARQL evaluation uses RDFLib’s built-in 1.1 engine. Dependencies are limited to RDFLib plus optional utilities (SPARQLWrapper, pandas, tabulate). Reproduction consists of creating a virtual environment, installing requirements.txt, and running the domain test scripts. Semantically, we model temporal intervals as half-open [start, end), so “current referent” resolution selects the unique binding with start ≤ t < end—operationalizing the mapping m(t) in Figure 1, aligning with the structural constraints in Figure 2.3, and verified by the competency questions in Tables 3 and 4. 4.2. Financial Derivatives Validation
Current Referent Resolution (CQ1): SELECT ? c o n t r a c t WHERE { ex : CL1 : h a s T e m p o r a l B i n d i n g ? b i n d i n g . ? b i n d i n g : b i n d s T o ? c o n t r a c t ; : h a s V a l i d T i m e / : h a s S t a r t T i m e ? s t a r t ; : h a s V a l i d T i m e / : hasEndTime ? end .
FILTER (NOW( ) >= ? s t a r t && NOW( ) < ? end ) }
Transition Tracking (CQ3): SELECT ? t i m e s t a m p ? from ? t o ? r u l e WHERE { ? r o l l a f d : C o n t r a c t R o l l ; : h a s T i m e s t a m p ? t i m e s t a m p ; f d : r o l l s F r o m ? from ; f d : r o l l s T o ? t o ; : t r i g g e r e d B y ? r u l e . } ORDER BY ? t i m e s t a m p 4.3. Air Transportation Validation
• CQ9: Track maintenance history for aircraft assigned to flight numbers • CQ10: Analyze crew rotation patterns across flights
Context reconstruction (CQ8): SELECT ? a i r c r a f t ? c a p t a i n ? p a s s e n g e r s ? s e v e r i t y WHERE { ? i n c i d e n t a avo : S a f e t y I n c i d e n t ; avo : r e p o r t e d F o r ? o p e r a t i o n ; avo : h a s S e v e r i t y ? s e v e r i t y . ? o p e r a t i o n avo : h a s A i r c r a f t ? a i r c r a f t ; avo : hasCrew / avo : hasMember ? c a p t a i n .
? c a p t a i n avo : h a s R o l e ex : C a p t a i n R o l e .
OPTIONAL { ? m e t r i c : o b s e r v e d R e f e r e n t E n t i t y ? o p e r a t i o n ; avo : h a s P a s s e n g e r C o u n t ? p a s s e n g e r s } }
Maintenance tracking (CQ9): SELECT DISTINCT ? a i r c r a f t ? maintType ? maintTime WHERE { ex : UA001 : h a s T e m p o r a l B i n d i n g / : bindsTo ? o p e r a t i o n . ? o p e r a t i o n avo : h a s A i r c r a f t ? a i r c r a f t . ? maint avo : i n v o l v e s A i r c r a f t ? a i r c r a f t ; avo : hasMaintenanceType ? maintType ; : h a s O b s e r v a t i o n T i m e ? maintTime .
} ORDER BY ? a i r c r a f t ? maintTime 4.4. Results Summary
• 100% Coverage: All competency questions answered correctly • Temporal Integrity: No gaps or overlaps detected in the transitions • Extensibility: Domain-specific questions handled without pattern modification
Having validated our pattern, we now position it relative to existing temporal modeling approaches to
clarify our contribution.
5.1. Temporal Qualification vs. Temporal Indirection
Existing temporal approaches can be grouped into four main categories, each revealing the same
limitation: they assume identifier-referent relationships remain static within temporal boundaries.
Time-indexed relations built on OWL-Time [
The reassignable identifier is defined as “an identifier that uniquely identifies something for a given time period, and that may be reused to identify something else at a diferent point in time,” with properties hasAssignmentTerminationDate and hasInitialAssignmentDate that apply directly to the identifier itself. This models scenarios where identifiers are recycled after periods of non-use (like vanity license plates transferred between vehicles), creating temporal gaps between assignments. However, rolling generic tickers like “CL1” exhibit fundamentally diferent semantics: the identifier maintains continuous existence without assignment/termination dates, while the referent contracts transition seamlessly according to exchange rules. The reassignable identifier’s cardinality constraints (max 1 for both assignment dates) enforce discrete reuse periods rather than continuous rule-based transitions.
sequences, or support the dual attribution required for market observations. The Temporal Indirection
bounds) from temporal bindings (which manage the time-dependent referent relationships), enabling the continuous, rule-governed referent evolution that characterizes financial rolling contracts.
6.1. Summary of Contributions This paper presented the Temporal Indirection Ontology Design Pattern, addressing a previously unrecognized gap in temporal knowledge representation. Our contributions include: • Conceptual Framework: Formal separation of persistent identifiers from evolving referents through temporal bindings • Reusable Pattern: Domain-independent abstractions validated across finance and aviation • Competency Questions: Support for current referent resolution, historical reconstruction, and audit trails • Open Implementation: Reference ontologies and validation suites for community adoption
6.2. Implications Temporal indirection appears wherever systems require stable references to evolving entities. Beyond our validated domains, potential applications include: • Healthcare: Clinical roles, on-call assignments, equipment allocation • Government: Organizational positions, regulatory interpretations, policy versions • Technology: API versions, service endpoints, deployment configurations 6.3. Future Directions Future work will extend the foundation by (a) developing a full axiomatization in Description Logic with temporal semantics, supported by reasoning complexity analysis and integration with temporal logic frameworks, (b) conducting performance and scalability benchmarks with large datasets, and (c) exploring template-based instantiation with Reasonable Ontology Templates (OTTR) [15] to streamline adoption by domain experts. We also plan to explore comparative testing of triplestore implementations, characterizing query behavior and identifying optimizations that can support more eficient resolution in temporal indirection scenarios.
healthcare, and other domains, enabling consistent modeling of roles, identifiers, and evolving entities. In conclusion, the Temporal Indirection Ontology Design Pattern provides a principled solution to representing temporal indirection in ontologies—a previously missing element in the ontology design patterns toolkit.
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