OBD Reasoner

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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

Classes, instances, relations

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: instances, or 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).

Conjunction and Implication

  • The double arrow (<math>\Rightarrow</math>) is also called directional implication. It can be translated into English to mean "it implies" or "it follows."
  • 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.

Quantification of instances

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(A, Puppy) <math>\Rightarrow</math> instance_of(A, Dog) -- (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." 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. The formulation as is_a(Puppy, Dog) is a class-level abstraction from the quantified instances we have used in (1).

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

The existential quantifier (<math>\exists</math>) 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(A, Bird) <math>\and</math> instance_of(A, Flightless thing) -- (3)

This can be translated to plain English to:

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

These are just some of the many constructs from first order logic which find common use in the Phenoscape project. There is a more full-fledged introduction to FOL on Wikipedia.

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.

Decomposing "post-composition" relations

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

Phenoscape-specific rules

This section describes the Phenoscape-specific rules added to the OBD reasoner.

PATO Character State relations

The Phenotypes and Traits Ontology (PATO) contains definitions of qualities, many of which are used in phenotype descriptions. These qualities are partitioned into various subsets (or slims) such as attribute slims, absent slims, and value slims. Attribute and value slims are mutually exclusive subsets. Attribute slims include qualities that correspond to Characters of anatomical entities, Color or Shape for example. Value slims include qualities, which correspond to States that a Character may take, for example Red and Blue for the Color character and Curved and Round for the Shape character. These relationships are not explicitly defined in the PATO ontology but can be inferred using the relations shown below

  1. PATO:0000587 oboInOwl:inSubset value_slim
  2. PATO:0000587 OBO_REL:is_a PATO:0000117
  3. PATO:0000117 oboInOwl:inSubset attribute_slim

From these definitions, the relationship

  1. PATO:0000587 PHENOSCAPE:value_for PATO:0000117

can be inferred by the reasoner. Ideally, the inference rule for this can be represented as

Rule: <math>\forall</math>V, A: in_Subset(V, value_slim) <math>\and</math> is_a(V, A) <math>\and</math> in_subset(A, attribute_slim) <math>\Rightarrow</math> value_for(V, A)

However, not all qualities are partitioned into one of the attribute or value slim subsets. In such cases, the super quality of these qualities is discovered by the reasoner and checked to find out if it is in the attribute or value slim subsets. This process continues until a quality belonging to the attribute slim subset is found. This can be represented as

Rule: <math>\forall</math>V, A: NOT in_subset(V, value_slim) <math>\and</math> is_a(V, A) <math>\and</math> in_subset(A, attribute_slim) <math>\Rightarrow</math> value_for(V, A)

Lastly, there are orphan qualities in PATO which are not related to any other qualities by subsumption and which do not belong to the attribute or value slim subsets. These are grouped under an unknown or undefined attribute.

Rule: <math>\forall</math>V, A: NOT in_Subset(V, value_slim) <math>\and</math> NOT is_a(V, A) <math>\Rightarrow</math> value_for(V, unknown attribute)

The Balhoff rule

Rule: <math>\forall</math>A, B, x: is_a(A, B) <math>\and </math>exhibits(A, x) <math>\Rightarrow</math> exhibits(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 a 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.

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.

Future directions

Possible future directions for the extension of the reasoner include adding more relation properties as well as some outstanding technical issues.

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