OBD Reasoner

The OBD reasoner uses definitions of transitive relations, relation hierarchies, and relation compositions to infer implicit information. These inferences are added to the OBD Phenoscape database. This section documents the inherited code in Perl and embedded SQL, that extracts implicit inferences from the downloaded ontologies and annotations of ZFIN and Phenoscape phenotypes.

Notation

When describing rules below, we use the following notations:

• A, B, C: classes (as subjects or objects). Note that relationship concepts can also appear as subject or object in an assertion.
• a, b, c: individuals (as subjects or objects)
• R: relationship (predicate)
• R(A, B): A R B, for example is_a(A, B) is equivalent to A is_a B. This is the functional form of assertions.
• Reification: assertions about assertions. I.e., A, B, ... may also be assertions. For example, the yellow that inheres_in a particular dorsal fin is_a yellow, which we can write formally as: is_a(inheres_in(yellow, dorsal_fin), yellow).

Upside down A's (<math>\forall</math>) and double arrows (<math>\Rightarrow</math>) translated

In first order logic (FOL), it is common to assert statements about all possible instances of a concept in the real world. Let us start with the assertion, "All puppies are dogs." This can be stated as shown below in (1)

<math>\forall</math> A: instance_of(Puppy, A) <math>\Rightarrow</math> instance_of(Dog, A) -- (1)

The inverted A (<math>\forall</math>) is called the universal quantifier and can be translated to "for every" or " for all" in plain English. Similarly, the colon (:) in the FOL statement above can be read as "such that." The double arrow (<math>\Rightarrow</math>) is also called directional implication. It can be translated into English to mean "it implies" or "it follows." Therefore, the sentence above translated into English reads:

"For all A such that A is a Puppy, implies that A is a Dog"

or even simpler as we shall readily comprehend, "All puppies are dogs." Note this is a simple assertion of the semantics of the is_a predicate that is so common to Phenoscape. Everyone will understand is_a(Puppy, Dog). The is_a relation is an upward abstraction from the quantified instances we have used in (1).

The "cap" or "A minus the stripe" (<math>\and</math>) is the FOL construct to specify conjunction and can be translated to "and" in plain English. The FOL statement below states the transitive property of the is_a relation

<math>\forall</math> A, B, C: is_a(A, B) <math>\and</math> is_a(B, C) <math>\Rightarrow</math> is_a(A, C) -- (2)

The statement (2) above can be translated to read:

For all A, B, and C, such that A is a B, and B is a C, it follows that A is a C

Lastly, we discuss the <math>\exists</math> (inverted E) operator, officially known as the existential quantifier, which can be translated to "there exists" or "at least" in plain English. Now consider the statement, "Some birds are flightless" This can be stated as shown below

<math>\exists</math> A: instance_of(Bird, A) <math>\and</math> instance_of(Flightless_Bird, A) -- (3)

This can be translated to plain English to:

"There exists an A such that A is a Bird and A is a Flightless Bird"

These are just some of the many constructs from first order logic which find common use in the Phenoscape project. For a full fledged introduction to the joys of FOL, click here.

A brief discussion on the pros and cons of existential and universal quantification

Universal quantification is a very rigid constraint, especially in the context of the life sciences. Consider the fact that all taxa descended from Ostariophysi possess basihyal cartilage, EXCEPT Siluriformes. This can be stated (we'll defer from using proper mathematical logic for now) with Existential Quantification as

Some Ostariophysi have Basihyal Cartilage (Assertion 1)

If the assertions Siluriformes are Ostariophysi and Siluriformes do not have Basihyal Cartilage were to be added to the assertion above, it is straightforward to see a contradiction will be avoided in the data. If Assertion 1 was changed to All Ostariophysi have Basihyal Cartilage, then a contradiction (or an inconsistency would be entailed).

Implemented Relation Properties

Relation Transitivity

Rule: <math>\forall</math>A, B, C, R and R transitive: R(A, B) <math>\and</math> R(B, C) <math>\Rightarrow</math> R(A, C)

Transitive relationships are the simplest inferences to be extracted and comprise the majority of new assertions added by the reasoner. When the ontologies are loaded into the database, every transitive relation is marked with a specific value of a property called is_transitive prior to loading. Transitive relationships include (ontology in brackets):

• is_a (OBO Relations)
• has_part (OBO Relations)
• part_of (OBO Relations)
• integral_part_of (OBO Relations)
• has_integral_part (OBO Relations)
• proper_part_of (OBO Relations)
• has_proper_part (OBO Relations)
• improper_part_of (OBO Relations)
• has_improper_part (OBO Relations)
• location_of (OBO Relations)
• located_in (OBO Relations)
• derives_from (OBO Relations)
• derived_into (OBO Relations)
• precedes (OBO Relations)
• preceded_by (OBO Relations)
• develops_from (Zebrafish Anatomy)
• anterior_to (Spatial Ontology)
• posterior_to (Spatial Ontology)
• proximal_to (Spatial Ontology)
• distal_to (Spatial Ontology)
• dorsal_to (Spatial Ontology)
• ventral_to (Spatial Ontology)
• surrounds (Spatial Ontology)
• surrounded_by (Spatial Ontology)
• superficial_to (Spatial Ontology)
• deep_to (Spatial Ontology)
• left_of (Spatial Ontology)
• right_of (Spatial Ontology)
• complete_evidence_for_feature(Sequence Ontology)
• evidence_for_feature (Sequence Ontology)
• derives_from (Sequence Ontology)
• member_of (Sequence Ontology)
• exhibits (Phenoscape Ontology)

Transitive relations are extracted from the database by the reasoner and transitive relationships are computed by the reasoner for each relation. For example, given that is_a is a transitive relation, and if the database holds A is_a B and B is_a C, then the reasoner computes A is_a C and adds this new assertion to the database. Similarly, new inferred assertions are added to the database for every transitive relation.

Note

Relation transitivity is the only relation property whose definition is (indirectly) extracted by the reasoner from the loaded ontologies (using the is_transitive metadata tag) in order to compute inferences. Although definitions of many of the other relation properties (such as relation reflexivity) can be found in the ontologies as well, in the current implementation inference mechanisms associated with these relation properties are hard coded into the reasoner.

Relation (role) compositions

Rule: <math>\forall</math>A, B, C, R: R(A, B) <math>\and</math> is_a(B, C) <math>\Rightarrow</math> R(A, C)

Rule: <math>\forall</math>A, B, C, R: is_a(A, B) <math>\and</math> R(B, C) <math>\Rightarrow</math> R(A, C)

Relation (role) compositions are of the form A R₁ B, B R₂ C => A (R₁|R₂) C. For example, given A is_a B and B part_of C then A part_of C. The reasoner computes such inferences and adds them to the database.

is_a Relation Reflexivity

Rule:<math>\forall</math>A, R and R reflexive <math>\Rightarrow</math> A R A

Reflexive relations relate their arguments to themselves. A good example: "A rose is_a rose." The is_a relation is reflexive. In the database, every class, instance, or relation (having a corresponding identifier in the Node table of the database) is inferred by the reasoner to be related to itself through the is_a relation. Given a class called Siluriformes (with identifier TTO:302), the reasoner adds the TTO:302 is_a TTO:302 to the database.

The subsumption (is_a) relation is the only reflexive relation that is handled by the reasoner. Other reflexive relations abound in the real world, subset_of is a good mathematical example from the domain of set theory. Every set is a subset of itself. Such relations are NOT dealt with by the reasoner.

Relation Hierarchies

Rule: <math>\forall</math>A, B, R₁, R₂: R₁(A, B) <math>\and</math> is_a(R₁, R₂) <math>\Rightarrow</math> R₂(A, B)

An example: If A father_of B and father_of is_a parent_of, then A parent_of B

Relation Chains

Rule: <math>\forall</math>A, B, C: inheres_in(A, B) <math>\and</math> part_of(B, C) <math>\Rightarrow</math> inheres_in_part_of(A, C)

Relation chains are a special case of relation composition. Component relations are accumulated into an assembly relation. Specifically, instances of the relation inheres_in_part_of are accumulated from instances of the relations of inheres_in and part_of. IF A inheres_in B and B part_of C, THEN A inheres_in_part_of C. This relation chain is specified by a holds_over_chain property in the inheres_in_part_of stanza of the Relation Ontology. However, the actual rule is hard coded into the OBD reasoner and not derived from the ontology.

Relation Intersections

Rule: <math>\forall</math>Q, E: inheres_in(Q, E) <math>\Rightarrow</math> inheres_in(inheres_in(Q, E), E)

Rule: <math>\forall</math>Q, E: inheres_in(Q, E) <math>\Rightarrow</math> is_a(inheres_in(Q, E), Q)

Phenotype annotations are typically "post-composed", where an entity and quality are combined into a Compositional Description. For example, an annotation about the quality decreased size (PATO:0000587) of the entity Dorsal Fin (TAO:0001173) may be post-composed into a Compositional Description that looks like PATO:0000587^OBO_REL:inheres_in(TAO:0001173). Instances of is_a and inheres_in relations are extracted from post compositions like this. In the above example, the reasoner extracts:

1. PATO:0000587^OBO_REL:inheres_in(TAO:0001173) OBO_REL:inheres_in TAO:0001173, and
2. PATO:0000587^OBO_REL:inheres_in(TAO:0001173) OBO_REL:is_a PATO:0000587

Relation Properties to be implemented

The following relation properties may be implemented on the reasoner in future if necessary.

Relation Symmetry

Rule: <math>\forall</math>A, B, R and R symmetric: R(A, B) <math>\Rightarrow</math> R(B, A)

An example of a symmetric relation is the neighbor relation. IF Jim neighbor_of Ryan THEN Ryan neighbor_of Jim. A more biologically relevant example is the in_contact_with relation. IF middle_nuchal_plate in_contact_with spinelet, THEN spinelet in_contact_with middle_nuchal_plate

NOTE: There is no direct relationship between relation symmetry and relation reflexivity

Relation Inversion

Rule: <math>\forall</math>A, B, R₁, R₂: R₁(A, B) <math>\and</math> inverse_of(R₁, R₂) <math>\Rightarrow</math> R₂(B, A)

An example of relation inversions can be found in the posterior_to and anterior_to relations. IF anterior_nuchal_plate anterior_to middle_nuchal_plate AND anterior_to inverse_of posterior_to, THEN middle_nuchal_plate posterior_to anterior_nuchal_plate

The Balhoff rule

Rule: <math>\forall</math>A, B, X, R: R(A, X) <math>\and</math> is_a(A, B) <math>\Rightarrow</math> R(B, X)

This rule was proposed by Jim Balhoff to reason upwards in a (typically taxonomic) hierarchy using the exhibits relation. A relevant example: GIVEN THAT Danio rerio exhibits a round fin AND Danio rerio is a Danio THEN Danio exhibits round fin. Note that exhibits has someOf semantics - so the inference is that some of Danio exhibit the phenotype.

This is the exact opposite of the genus differentia rule which postulates reasoning only downwards in a hierarchy. The relevance of this rule to the Phenoscape project needs to be discussed.

• In our use-case, A and B are terms from a species taxonomy, and R is the exhibits relation.
  • Should the above rule be narrowed to only hold for exhibits, rather than for any relation R?
  • Should the rule be narrowed to require that A and B be from a species taxonomy (if so, how would one codify that in first-order logic?), or would that be implied if R is narrowed to exhibits? For example, would the rule still hold is A and B are genotypes?
• As we reason upwards the taxonomy using this rule, we would accumulate ultimately the union of all annotated phenotypes for the root species node. Is this useful?
• Once we change the species taxonomy to use the member_of relation in place of the is_a relation, would the above rule still apply? In fact, would it apply then in a cleaner way, in the sense of being more compatible with the semantics of member_of compared to is_a?

The problem with absence of features

Descriptions of phenotypes as used in the Phenoscape project (and a plethora of phenomena in the real world) are replete with exceptions, or aberrations from what is considered to be "normal." While canonical ontologies like the FMA and the TAO contain ontological definitions of ideal specimens, observations in the life sciences are full of aberrations to these general rules.

Phenoscape has some typical issues dealing with absence of anatomical features in certain species of Ostariophysian fishes. For example, the basihyal cartilage is found in all species of Ostariophysian fishes, except the Siluriformes. At present, this information is captured in Phenoscape using the combination of the PATO term for "absent in organism" (PATO:0000462), the "inheres_in" relation from the OBO Relations Ontology, the TAO term for "basihyal cartilage" (TAO:0001510), the "exhibits" relation from the PHENOSCAPE ontology, and the TTO term for Siluriformes (TTO:1380). This is shown below.

<javascript> TTO:1380 PHENOSCAPE:exhibits PATO:0000462^OBO_REL:inheres_in(TAO:0001510) </javascript>

In plain English, this translates to "Siluriformes exhibit absence in organism which inheres in basihyal cartilage." The semantics of this sentence are vague to say the least. Going by this method, it is impossible to state that basihyal cartilage is absent in Siluriformes without referring to at least one instance of basihyal cartilage. Combining a quality absent with a feature through the inheres_in property is very misleading in itself (ex: absence inheres in cartilage), contorting the intrinsic semantics of the inheres_in relation. These problems have been discussed in Ceusters et al and Hoehndorf et al. Both these publications propose solutions to integrate these aberrant observations with canonical definitions, without causing inconsistencies in reasoning procedures.

Another issue specific to the Phenoscape project was raised by Paula at the SICB workshop. Given that basihyal cartilage is absent in Siluriformes, basihyal bone should be absent in Siluriformes as well. This is because basihyal bone develops from basihyal cartilage. This may be inferred by adding a new relation chaining rule shown below to the OBD reasoner

Rule:<math>\forall</math>F1, F2, S: absent_in(F1, S) <math>\and</math> develops_from(F2, F1) <math>\Rightarrow</math> absent_in(F2, S)

This relation chain corresponds to the observation GIVEN THAT Basihyal_Cartilage absent_in Siluriformes AND Basihyal_Bone develops_from Basihyal_cartilage, THEN Basihyal_Bone absent_in Siluriformes. This and other similar relation chains (as per identified requirements) are to be implemented for the Phenoscape project in the future. Strategies to deal with absent features in general are also to be implemented in the near future.

Sweeps

A reasoner functions over several sweeps. In each sweep, new implicit inferences are derived from the explicit annotations (as described in the previous sections) and added to the database. In the following sweep, inferences added from the previous sweep are used to extract further inferences. This process continues until no additional inferences are added in a sweep. This is when the deductive closure of the inference procedure is reached. No further inferences are possible and the reasoner exits.