Status: intermediate draft

Authors and contributors:

• Chris Mungall (author)

Date: 2012

Document Type: ontology_design_pattern

A crucial part of anatomical knowledge concerns spatial disjointness. This article covers the concept of part-disjointness and how it is applied in Uberon

In anatomy ontologies, it can be useful to state that two parts are non-overlapping - they contain no parts in common. For example, we may want to model the limb such that the autopod, zeugopod and stylopod are spatially adjacent and have no parts in common (this does not mean that structures cannot overlap both).

In OWL, the statement X DisjointWith Y refers to the classes X and Y - it means there is nothing that instantiates both an X and a Y.

This means the following statements are anatomically correct:

1. manus DisjointWith forelimb
2. brain DisjointWith spinal cord

It also means that the following axioms do not lead to an inconsistency:

3. manus DisjointWith forelimb zeugopod
4. foo SubClassOf part_of some manus
5. foo SubClassOf part_of some forelimb zeugopod

This sometimes causes confusion, as users unfamiliar with OWL read disjoint as being spatially disjoint, which is not the case. Axiom (3) above states that nothing is both a manus and a forelimb zeugopod. It does not restrict how other entities relate to these classes via properties such as part_of.

We can in fact make statements of parthood-disjointness in OWL using General Class Inclusion (GCI) axioms, for example:

6. (part_of some manus) DisjointWith (part_of some forelimb zeugopod)

This states that there is nothing that is both part of a manus and part of a forelimb zeugopod. This can be written in an equivalent way:

7. (part_of some manus) and (part_of some forelimb zeugopod) EquivalentTo owl:Nothing

Using either (6) or (7) in conjunction with (4) and (5) leads to 'foo' being unsatisfiable.

Note that GCIs cannot be directly authored in obo-format, but we can specify them indirectly, by means of a shortcut relation:

  [Typedef]
  id: spatially_disjoint_from
  expand_assertion_to: "Class: <http://www.w3.org/2002/07/owl#Nothing> EquivalentTo: (BFO_0000050 some ?X) and (BFO_0000050 some ?Y)" []
  is_metadata_tag: true
  is_class_level: true

This means the ontology can contain 'silent' annotation assertions of the form:

  Class: `manus`
   Annotations: spatially_disjoint_from `forelimb zeugopod`

(which are written in obo-format using the relationship tag)

An extra step in the obo to owl conversion process will expand this to the correct OWL axiom.

Note that in classic mereology, the parthood relation is considered reflexive. This means that a statement:

• (part_of some X) DisjointWith (part_of some Y)

necessarily entails 'X DisjointWith Y' (as well as 'X DisjointWith part_of some Y' and its reciprocal).

However, working with reflexivity axioms poses some problems (outside the scope of this document, but briefly: global reflexivity axioms are too strong and cannot be used in conjunction with domain/range constraints; local reflexivity axioms of the form continuant SubClassOf part_of SELF should be used; also, fast reasoners such as Elk may not support these constructs, at least at the time of writing, and Uberon is heavily dependent on Elk for fast checking).

One possible approach to get around this limitation: generate a supplementary ontology with axioms of the form 'X part_of some X'; this could be hidden from the user, but imported as part of the Jenkins QC pipeline to check for spatial disjointness errors.

• http://ontogenesis.knowledgeblog.org/1288
• http://ontogenesis.knowledgeblog.org/1260
• https://docs.google.com/document/d/1cPWBqrl_Qy7XHEWFqtR_PgQX61yRkgGuLaiDpnEXxkE/edit#heading=h.cx8lslfjfyrl
• http://dx.doi.org/doi:10.1038/npre.2011.5292.2