Context

An applied ontology asks questions about its declared conditions before any instance data exists. Does a revised benefit profile admit anyone the previous revision did not? Do two trial arms admit overlapping patients? Does a profile admit anything at all? These are subsumption and satisfiability questions over classes. A DL reasoner answers them without an A-Box, so the open-world assumption does not distort the answers.

LATTICE has no backend that turns conditions into OWL classes. The SPARQL, SHACL and SWRL backends evaluate candidates. They cannot compare two conditions with each other.

Decision

An OWL backend on the shared IR. It reads the same plans as the other backends (ADR-A24, ADR-A89) and emits one generated OWL module per compilation as an exe:OwlArtefact, with the same provenance links as the existing artefacts. Each condition is expressed over the domain property that carries its candidate, as bound under ADR-A91.

Hierarchy classes. For a hierarchical dimension property R and each concept c of the resolved scheme edition, a primitive class Within_R(c):

∃R.{c} ⊑ Within_R(c)
Within_R(d) ⊑ Within_R(c)      for each d with d skos:broader c

Both axiom forms are in OWL 2 EL.

Sibling disjointness is a caller option. Within_R(c) ⊓ Within_R(c′) ⊑ ⊥ for siblings c and c′ is emitted only when the caller declares the scheme’s siblings mutually exclusive and R functional. The option is recorded in the artefact’s provenance. Without it, the checks in item 6 report an overlap or an expansion that disjointness would rule out, and never miss one.

Condition classes. For subject class S:

Cond ≡ S ⊓ (⊔ᵢ Within_R(rᵢ)) ⊓ ¬(⊔ⱼ Within_R(eⱼ))

A condition with exclusions only uses the scheme’s top concepts in place of the required set (L12). An interval condition becomes a datatype restriction on its value property, one property per unit, with no conversion. A candidate strictly above an excluded concept is neither entailed in nor out of Cond, which is the design-time reading of L11.

Profile classes. AllRequired is intersection and AnySufficient is union. DimensionConsistent is refused, as in ADR-A89.

Checks. A library function and CLI answer three questions over the generated module: subsumption (P′ ⊑ P), satisfiability of P, and satisfiability of P ⊓ Q. Each answer is recorded with the module’s provenance. The checks run through the ADR-A83 reasoning harness and never through a reasoner declared as a product dependency.

Expressivity is declared. Hierarchy axioms stay in EL. Condition and profile classes use negation, union and datatype restrictions, within OWL 2 DL. Each generated module states which of the two it contains.

Consequences

Executable gains exe:OwlArtefact and a check-result record, a MINOR bump.

The backend cannot be verified until the ADR-A83 harness exists. The repository’s reasoning extra provides an OWL RL engine only.

Generated class names derive deterministically from condition and concept IRIs, so regeneration after an unchanged edition yields identical modules.

These classes answer design-time questions. Runtime decisions stay with the SPARQL reference backend.

Open questions

Should sibling exclusivity become a Vocabulary declaration on a scheme edition, rather than a compile option? It is a fact about the scheme, which argues for the graph. It would also be a Vocabulary MINOR bump that cascades to every layer. This ADR recommends the compile option until a second consumer needs the declaration.

Addendum (2026-09-25): conditions read through evidence paths

Resolved: option B, chosen by the human on 2026-09-25.

This ADR encodes a condition over one dimension property R. ADR-A91 lets a condition read its candidate through a path of several steps, and a subject may have several values at its end. The SPARQL reference treats a subject with no value or several as Undetermined, and one with a single value by the decision table. Two OWL readings of an exclusion then differ: ¬∃path.Within(e) (no value is excluded) and ∃path.¬Within(e) (some value is not excluded). Neither reproduces “several values give Undetermined”, and the same gap affects inclusions.

Options:

A. Require functional properties. Compile only paths whose every step the applied ontology declares owl:FunctionalProperty (inverse steps: owl:InverseFunctionalProperty). The readings then coincide. This puts an OWL axiom on the applied ontology’s own properties.

B. Single-valued claim on the binding. The binding states that each step of its path yields at most one value (for example elg:singleValued true). The generated classes build the claim in with a cardinality at each step (≤1 p₁ ⊓ ∃p₁.(≤1 p₂ ⊓ ∃p₂.Within(c))), and a generated SHACL shape checks the same per-step claim on data, so the classes and the data agree. The applied ontology’s properties are untouched, and a path the author does not claim single-valued is refused.

C. No restriction. Choose the ∃ reading and document that design-time answers describe “some value” semantics, which differ from runtime decisions for subjects with several values.

SKOS is not involved in any option. skos:broader is used only inside the hierarchy classes of item 2, which allow several broader concepts per concept. The restriction concerns the path from a subject to its candidate, which belongs to the applied ontology, not to the concept scheme.

Implementation notes (2026-09-25, AOR-10 and AOR-11)

tools/mork_compilers/src/mork_compilers/owl_backend.py. Within(c) is a class of concepts, with {c} ⊑ Within(c). Item 2’s Within_R(c) is ∃R.Within(c) at the path’s last step R, so one hierarchy serves every property that reads the scheme.

Flat strategies use nominals. Every concept a module names is declared distinct (owl:AllDifferent), matching the SPARQL reference’s comparison by IRI.

Sibling disjointness treats a scheme’s top concepts as siblings, and is refused for a member with several broader concepts, where it would make that member’s nominal inconsistent.

Interval conditions restrict owl:real, on a qnt:Quantity’s numeric value or on the literal where the binding reads on the condition’s space.

One module per compilation. Several plans may share one, which the checks need. A concept whose broader concepts differ between the plans’ schemes is refused.

Every module is declared OWL 2 DL. The per-step ≤1 restriction of option B is outside EL, so no condition class is in EL.

Each claimed binding gets a shape with sh:maxCount 1 on each prefix of its path, which is the per-step claim for every node reached from a subject.