📄 Expressing OWL axioms by English sentences: dubious in theory, feasible in practice

Summary

Tools that verbalise OWL ontologies in controlled English usually assume that each axiom can become one sentence, with atomic terms realised through a lexicon. Power and Third ask whether this assumption holds. In principle it can fail in three ways. Some functors describe properties in a mathematical way that everyday English handles poorly. OWL gives an axiom no topic–comment structure. Nesting can pack unlimited content into a single axiom. To see how ontology authors actually write, the authors analysed a corpus of 203 ontologies containing 633,791 axioms. They abstracted away atomic identifiers and counted functor and argument patterns. The problems turned out to be rare. A few simple patterns make up almost all axioms. The hard property functors are uncommon. When one argument is complex, the atomic argument nearly always comes first. Authors therefore treat axioms much like sentences, which makes generic sentence-per-axiom verbalisers workable. The frequency list also shows which patterns a future reader study should prioritise.

Key points

• The corpus contains about 200 ontologies (203) and 633,791 axioms. SubClassOf alone makes up 74.0% of axioms (468,812).
• The three most frequent patterns are:
  • SubClassOf(Class,Class) at 46.9%
  • SubClassOf(Class,ObjectSomeValuesFrom(ObjectProperty,Class)) at 25.0%
  • DisjointClasses(Class,Class) at 14.9%
• Pattern coverage is highly concentrated: 91.9% of axioms fall under the five most common patterns, 95.8% under the ten most common, and 97.2% under the twenty most common.
• In SubClassOf, only 978 axioms (0.2%) have a complex first argument. In mixed simple/complex axioms, the atomic argument always appears first.
• The 16 common functors split into two groups. Class and individual axioms are easy to verbalise, while property axioms (Transitive, Functional, Inverse, and similar) are hard. None of the hard ones appears in the top ten patterns.
• The work was part of the SWAT project. The authors plan a follow-up study of how human readers interpret alternative sentence templates.

Interesting ideas

• I1. Before arguing that a formal-to-text mapping is impossible in theory, measure which constructions people actually use; a long tail of awkward cases matters little if each is rare and isolated.
• I2. Argument order can reveal implicit information structure: when authors consistently put the atomic term first, that term acts as the topic and the complex expression as the comment.
• I3. Abstracting identifiers away to count structural "signatures" (functor plus argument types) gives a compact inventory of what must be handled.
• I4. Equivalence axioms mostly follow the classical genus-plus-differentia definition, which maps neatly onto one sentence: "an X is a Y that does Z".
• I5. Any set of axioms can be merged into one unreadable mega-axiom, so readability depends on how content is distributed across statements, not only on logic.

For Mova

How these ideas could serve Mova, our small open language model — its files, stages and tests:

• I1 (back): Rank meaning-graph configurations by corpus frequency and polish generation templates for the top ones first, accepting clumsy but correct output for rare ones.
• I2 (back): When generating from a graph, choose as subject the simplest, most entity-like node and push complex material into the predicate, as ontology authors do.
• I3 (world): Count signatures of the compiled ontology and knowledge-graph facts the same way to see which relation shapes dominate and need first-class reasoning support.
• I4 (world): Store definitions imported from WordNet/Wikidata in genus–differentia form so they can be reasoned over and read back in one sentence.
• I5 (back): The text → graph → text compressor should split content into topic-sized units per sentence rather than emitting maximally merged clauses.