As we know that functions (1 to 1) are different from relations (1 to many). All functions are relations, but not all relations are functions. In the case of creating an ontology for biology, we use relations. But, in biology, is it possible to apply the functions as well. Can there be any such relation which is a function in the case of biomedical ontology. For example, part-of, composed-of, located-in, surrounded-by, etc. are all relations in the context of biomedical ontology. Or do we have to always understand biology ontology in terms of relations only and not functions.
Prof. Barry Smith (University of Buffalo) clarifies the distinction between ontology of relations and the way relations and functions are treated in a set theory. Further he emphasizes on the functional associations (in mathematical sense) can occur in process relations. For example, process-a regulates process-b.
Now this sounds interesting. In this case, I think, some of the process relations can be functional. Such process relations are : regulates, transforms into, derives from, develops into, preceded by, results into, etc.
Let me illustrate with a few assertions:
Larva transforms into pupa
zygote develops into foetus
blastula transforms into gastrula
What I am trying to point out is that the domain and range for these process relations will always be of 1 to 1 mapping. So, these process relations can be of functional type.
But the structural relations such as part of, surrounded by can not be of functional type as a domain can have many ranges in such relations.
P.S. This post is based on my discussion on relations and functions in biology on the OBO mailing list.