# OBD Reasoner

**The tool or documentation in this page is obsolete.** The rule-based OBD reasoner is used within the OBD-powered database. The current version of the Phenoscape KB is not powered anymore by OBD.

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.

## Contents

## 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 *R*_{1} B, B *R*_{2} C => A (*R*_{1}|*R*_{2}) 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, *R _{1}*,

*R*:

_{2}*R*(A, B) <math>\and</math>

_{1}*is_a*(

*R*,

_{1}*R*) <math>\Rightarrow</math>

_{2}*R*(A, B)

_{2}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:

- PATO:0000587^OBO_REL:inheres_in(TAO:0001173) OBO_REL:inheres_in TAO:0001173, and
- 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

- PATO:0000587 oboInOwl:inSubset value_slim
- PATO:0000587 OBO_REL:is_a PATO:0000117
- PATO:0000117 oboInOwl:inSubset attribute_slim

From these definitions, the relationship

- 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, *R _{1}*,

*R*:

_{2}*R*(A, B) <math>\and</math>

_{1}*inverse_of*(

*R*,

_{1}*R*) <math>\Rightarrow</math>

_{2}*R*(B, A)

_{2}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