Novel reasoning strategies
Potential strategies to implement novel inference procedures introduced in the OBD Reasoner page. These comprise: the Balhoff rule and the Mabee rule for inferring the absence of features in taxa.
Prelude: Instance relations and class relations
For reasoning purposes , it is useful to conceptualize two separate entities in the real-world viz. classes and instances. Every entity in the real world is an instance. Instances can be grouped together on the basis of the properties they exhibit, such as the things that are colorless. Classes are groupings or sets of instances on the basis of common properties that they exhibit. An example of a class would be car, which includes all the instances which comprise a chassis resting (typically) on 4 wheels which is powered by an internal combustion engine.
Subsumption semantics (as inherent in the is_a relation) hold between sets of real-world instances or classes. For example, the set of all left-handed people above the age 35 is subsumed by the set of all the people above the age 35 (who may be left- or right-handed or ambidextrous). The subsumption semantics of the is_a relation are defined in the OBO relations ontology as follows: "...C is_a C' if and only if: given any c that instantiates C at a time t, c instantiates C' at t..." In plain English, this means: the set of all left-handed people above the age 35 is subsumed by (or included by) the set of people above 35 if and only if, a person who belongs to the group of left handed people above the age of 35 also belongs to the set of people above the age of 35. This is trivially valid in the real world. The relation is_a is therefore a class relation. On the other hand, exhibits is what can be called an instance relation, because it relates real-world instances of taxa to actual phenotypes.
The Balhoff rule
The Balhoff rule can be summarized as follows. "IF SOME instances of a species A exhibits a phenotype P, AND ALL instances of species A are also instances of species B, THEN SOME instances of species B exhibit phenotype P." Using FOL constructs, this can be represented as shown below.
Rule: <math>\forall</math>A, B<math>\exists </math>X: is_a(A, B) <math>\and </math>R(A, X) <math>\Rightarrow</math> R(B, X)
In our use-case, A and B are terms from a species taxonomy, and R is the exhibits relation. Note that this rule is applicable to all relations that R represents. In the real world, if we know that some combustion engines have four cylinders (while some other have six), we can correctly deduce that some engines (which include both 4 cylinder and 6 cylinder engines) have four cylinders. The only constraint on this rule is that some kind of subsumption relationship hold between A and B. The is_a name of the relation can be conceivably replaced by kind-of for example; as long as the semantics of the relation implied subsumption or inclusion, the Balhoff rule would hold.
The inclusion of the Balhoff rule would lead to the extraction of inferences such as "SOME Ostariophysians exhibit increased thickness of hyoid bones and SOME Ostariophysians exhibit decreased thickness of hyoid bones." All these inferences are extracted from phenotype assertions about different species like Gonorhynchiformes and Cypriniformes that are subsumed by Ostariophysians.
