Ordered data needs to distinguish general precedence from value comparison and immediate adjacency. The Inferal Ordering Ontology provides named partial and total ordering contexts, broad precedes/follows relations, specialized less-than/greater-than relations, immediate neighbors, same-rank groups, and optional integer ranks without imposing one domain-specific comparison algorithm.
A numeric value can be greater than another value, a chapter can follow another chapter, and two adjacent workflow states can immediately precede and follow one another. These statements have related order structure, but they are not interchangeable. In particular, a greater value follows a lesser value in the canonical orientation of that comparison scale; it does not necessarily appear later in an arbitrary descending presentation.
This ontology exposes the shared strict-order structure while retaining the narrower meanings. Broad precedence supports sequences and other ordered resources that have no useful less-than or greater-than interpretation. Comparison properties specialize broad precedence for resources with comparative values. Immediate properties add an adjacency claim that is intentionally not transitive.
The intended audience is vocabulary authors who need reusable ordering relations, graph producers that publish explicitly scoped order data, validators that check ordering integrity, and processors that traverse or materialize relation closure.
The ontology owns contextual membership, broad and specialized strict order relations, immediate adjacency, same-rank grouping, optional integer ranks, and validation of their structural consistency.
It does not define arithmetic comparison, lexical collation, calendar conversion, temporal interval topology, version precedence algorithms, priority policy, or presentation sorting. It does not derive ordering edges from rank values. Domain vocabularies and processors remain responsible for those rules.
An ordering describes one canonical orientation. A descending display, reverse traversal, or another application-specific presentation does not change comparative truth and SHOULD be represented as a separate ordering participation when it must be expressed as RDF.
This is an unofficial 0.1 Editor's Draft maintained in the Inferal ontology repository.
Feedback should be sent to contact@inferal.com.
This specification defines three conformance classes: ordering data graph, ordering producer, and ordering processor.
An ordering data graph is an RDF graph that uses the terms defined in this specification consistently with the term definitions and validation expectations below.
An ordering producer is software or an authoring process that emits ordering contexts, comparable resources, broad precedence, specialized comparisons, immediate adjacency, same-rank relations, or ranks.
An ordering processor is software that consumes an ordering data graph and validates, expands, or queries ordering relations. A conforming processor MUST keep ordering contexts isolated and MUST NOT infer ordering relations between resources that do not share an ordering.
| Prefix | IRI |
|---|---|
ord |
https://ontology.inferal.com/modules/ordering/ |
The Ordering Ontology is intentionally domain-neutral. It does not define numeric, lexical, temporal, version, priority, or policy-specific comparison rules. Domain modules MAY specialize these terms or provide rules and queries that emit ord:precedes, ord:follows, ord:greaterThan, ord:lessThan, ord:immediatelyPrecedes, ord:immediatelyFollows, ord:sameRankAs, or ord:rank.
| Term | Kind | Normative role |
|---|---|---|
ord:Comparable |
Class | A resource that participates in one named ordering context. |
ord:Ordering |
Class | A named, oriented context for ordered comparable resources. |
ord:PartialOrdering |
Class | An ordering context that permits pairs without a stated or entailed relation. |
ord:TotalOrdering |
Class | An ordering context in which every pair of distinct members is related by strict precedence or a same-rank relation. |
ord:inOrdering |
Object property | Associates a comparable resource with exactly one ordering context. |
ord:precedes |
Transitive object property | Broad strict precedence: the subject occupies an earlier, not necessarily adjacent, position. |
ord:follows |
Transitive object property | Broad strict precedence: the subject occupies a later, not necessarily adjacent, position; inverse of ord:precedes. |
ord:greaterThan |
Object property | Strict transitive comparative relation that specializes ord:follows. |
ord:lessThan |
Object property | Strict transitive comparative relation that specializes ord:precedes; inverse of ord:greaterThan. |
ord:immediatelyPrecedes |
Object property | Non-transitive asserted adjacency relation that specializes ord:precedes. |
ord:immediatelyFollows |
Object property | Non-transitive asserted adjacency relation that specializes ord:follows; inverse of ord:immediatelyPrecedes. |
ord:sameRankAs |
Object property | Symmetric and transitive relation stating that comparable resources occupy the same ordering position without asserting identity. |
ord:rank |
Datatype property | Optional integer rank attached to a comparable resource. |
ord:RankDirection |
Class | The direction in which numeric ranks determine comparison within an ordering context. |
ord:AscendingRank |
Individual | Rank direction in which the member holding the greater ord:rank is the greater of the pair. |
ord:DescendingRank |
Individual | Rank direction in which the member holding the greater ord:rank is the lesser of the pair. |
ord:rankDirection |
Object property | States that ranks determine comparison within an ord:Ordering, and in which direction. Two members that both carry a ord:rank in a rank-directed ordering are comparable without an asserted ord:greaterThan or ord:lessThan edge between them. |
An ord:Ordering names an oriented ordering context. Every ord:Comparable MUST have exactly one ord:inOrdering value. Ordering relations are meaningful only between comparable resources in the same ordering. This prevents accidental comparison between unrelated domains, such as priority levels, calendar releases, and semantic versions.
ord:precedes and ord:follows are the broad strict ordering relations. They are transitive and inverse of each other. Precedence describes relative position and does not imply that two resources are adjacent or that their domain has a less-than or greater-than concept.
ord:lessThan specializes ord:precedes, and
ord:greaterThan specializes ord:follows. They are also
transitive and inverse of each other. Under RDFS or OWL subproperty
reasoning, A ord:lessThan B entails
A ord:precedes B, while
B ord:greaterThan A entails
B ord:follows A. The converse entailments do not hold.
The comparison hierarchy uses the canonical orientation of the named ordering. It does not claim that a greater value appears after a lesser value in every user interface or serialization. A descending presentation order is a separate positional context and MUST NOT be inferred by reversing comparative truth.
ord:immediatelyPrecedes specializes ord:precedes, and ord:immediatelyFollows specializes ord:follows. They are inverse but not transitive. An immediate assertion says that no other comparable resource lies between its endpoints in the ordering extent claimed by the producer. RDF absence alone cannot establish this closed-world adjacency claim.
Every strict relation in this section is irreflexive in conforming data
and MUST be acyclic across its combined strict-relation closure. If a
graph states A ord:immediatelyPrecedes B and
B ord:immediatelyPrecedes C, a reasoner can infer
A ord:precedes C, but it MUST NOT infer
A ord:immediatelyPrecedes C.
ord:sameRankAs groups comparable resources at the same comparison position without asserting RDF or OWL identity. It is symmetric and transitive. Those OWL characteristics entail reflexive same-rank links for resources in a non-trivial same-rank group, so conforming validation permits explicit or entailed self-links. A same-rank self-link is redundant and does not assert RDF or OWL identity.
ord:rank is an optional integer annotation. This ontology does not define whether larger or smaller rank values sort first, and it does not infer ordering relations from rank values. Producers that want rank-derived precedence, comparison, adjacency, or same-rank relations MUST document and apply domain-specific rules. If two comparable resources are connected by ord:sameRankAs and both assert ord:rank, their rank values MUST be equal.
The source validation profile constrains each ord:Comparable to exactly one ord:inOrdering value. If one conceptual item participates in multiple ordering contexts, producers SHOULD model each participation as a separate comparable resource and connect those resources with domain-specific identity or provenance terms.
ord:PartialOrdering is an ordering context in which some pairs of comparable resources MAY remain without a stated relation. Under open-world semantics, a missing edge means only that the graph does not state or entail the relationship; it does not prove that the resources are intrinsically incomparable.
ord:TotalOrdering is stricter. For every pair of distinct comparable resources that have the total ordering as their ord:inOrdering, the graph MUST provide or imply at least one of these relationships:
Because same-rank ties are allowed, ord:TotalOrdering represents a total preorder when same-rank groups are present and a strict total order when no same-rank groups are present.
Totality is a closed-world validation condition over the supplied data graph and its broad, comparative, immediate, inverse, and transitive closure. It does not prove that the producer supplied every resource in the real-world ordering.
This ontology declares ord:precedes, ord:follows, ord:greaterThan, and ord:lessThan as transitive properties. Processors MAY materialize inverse, subproperty, and transitive entailments. The immediate properties are not transitive, but their subproperty entailments participate in broad precedence closure.
The ontology also declares ord:sameRankAs as symmetric and
transitive. Processors MAY use ord:sameRankAs and its
inverse path to identify same-rank groups. The same-rank relation does
not by itself create strict ordering edges to or from every member of a
same-rank group; processors that need representative-based comparison
SHOULD define that query behavior explicitly.
A conforming ordering data graph MUST satisfy the following validation expectations:
xsd:integer.These checks are intentionally closed-world validation rules. They do not prove that a producer has supplied every intended comparable resource, that no unreported intermediate resource exists, or that domain-specific relations follow from rank values.
Domain vocabularies MAY specialize the broad or comparative properties when their relation has the same orientation and logical strength. A temporal relation, workflow dependency, causal relation, or display position MUST NOT be declared equivalent merely because it is described informally as “before” or “after.” Temporal interval relations in OWL-Time, for example, carry temporal-entity and boundary semantics that this ontology does not reproduce.
A conditional correspondence—such as projecting temporal precedence into one named timeline ordering—belongs in a domain profile or executable mapping. This ontology does not import or redefine external temporal vocabularies.