Absence Phenotypes in OWL

Phenotypes describing the absence of a type of structure require particular consideration for both semantic modeling and reasoning.

Basic EQ modeling

We generally represent phenotypes as classes describing relationships between an entity and a quality. The entity is usually an anatomical structure, such as a dorsal fin, which is the bearer_of some quality, such as an instance of serrated. The inverse of bearer_of is inheres_in, so we can either describe the set of organisms with this phenotype:

has_part some (dorsal fin and bearer_of some serrated)

or describe this class of phenotypes (from the perspective of the quality):

serrated and inheres_in some dorsal fin

These expressions are not equivalent but describe different aspects of the same data model.

"Absent" quality

The PATO ontology of phenotypic qualities includes a commonly used quality absent. However, using this term in the above EQ model is problematic. For the entity dorsal fin and the quality absent, we would end up with an expression such as:

has_part some (dorsal fin and bearer_of some absent)

The obvious problem is that this asserts the existence of a dorsal fin, needed to bear the instance of absent.

Additionally, reasoning with these classes produces unintuitive results. An organism with no dorsal fin would be described as has_part some dorsal fin and bearer_of some absent. An organism with no fins at all would be in the class has_part some fin and bearer_of some absent. An OWL reasoner would correctly infer that the former is a subclass of the latter, which is the opposite of what we really intend (organisms without dorsal fins are a superset of the organisms without any fins).

Using OWL class complements or cardinality

Instead of representing absence with a quality, we can describe it in OWL using a class complement (logical negation):

not (has_part some dorsal fin)

This results in reasoning that matches our expectations: not (has_part some fin) is a subclass of not (has_part some dorsal fin). Also, we don't infer the existence of a structure that is supposed to be absent. However, this approach introduces two difficulties. First, we lose the ability to directly describe the phenotypic quality (there is no instance of "absence" to refer to; we are instead describing the organism or structure). This can be problematic when the application otherwise presents or queries for phenotypes as qualities. Second, complement expressions are not available within the OWL EL profile. Reasoning with such expressions requires a complete OWL DL reasoner, which is far less scalable.

We could also use a cardinality expression:

has_part exactly 0 dorsal fin

This is logically equivalent to the complement expression, and cardinality expressions present the same difficulties just described. Also, while cardinalities other than 0 can be used to express counts, transitive properties such as has_part cannot be used in cardinality expressions (except possibly in the special case of cardinality 0).

"Lacks all parts of type" quality

The solution provided by PATO for the problems with the absent quality is the "relational" quality lacks all parts of type. Relational qualities in PATO are qualities that are further specified by a relation to another class, for example sensitivity toward ultraviolet light. So instead of describing an entity dorsal fin which bears an absent quality, we should instead describe the entity body which bears a quality lacks all parts of type toward dorsal fin. At first glance, this approach seems to address all the above issues:

• We can describe phenotypes from the quality perspective; lacks all parts of type is a subclass of quality and doesn't require use of a complement expression.
• The instance of lacks all parts of type inheres_in an instance of body (or other containing structure) rather than in a non-existent dorsal fin.

and...

• A lacks all parts of type toward fin should be a subclass of lacks all parts of type toward dorsal fin... but is it??

Defining an explicit OWL representation for lacks all parts of type introduces some reasoning difficulties. To relate the quality to the missing part, we might expect to use the standard existential restriction:

lacks all parts of type and inheres_in some body and towards some dorsal fin

However, we end up with the same backwards reasoning found with absent. lacks all parts of type towards some fin is a superclass of lacks all parts of type towards some dorsal fin, the opposite of what we intend. But an existential restriction on towards clearly holds the wrong semantics anyway (and furthermore implies the existence of the absent structure). The object of the towards relation is the type dorsal fin itself, not some instance. To reference the class directly we must use it in a value restriction, where we would expect an instance:

lacks all parts of type and inheres_in some body and towards value dorsal fin