>I am concerned about the excessive emphasis on hierarchy, i.e. the
>relations among unary predicates, in discussions of ontology. I think
>the lack of mastery of non-unary predicates is more of an obstacle to
>use of the ontologies.
>For example, what about "x is between y and z" in its various
>sentences?
That is indeed an important issue. In the vocabularies of natural languages
(which are the starting points for all of our ontologies, even the most
highly formalized ones), the words that map to monadic predicates tend
to dominate -- nouns and adjectives. But the words that present the
most complexity are the verbs, with prepositions and conjunctions
creating quite a few problems as well.
However, the relational words also fall into hierarchies. In particular,
all of the thematic roles (or case relations) associated with verbs can
be classified as subtypes of Participant, further subdivided along the
lines of Aristotle's four "causes" (or "aitiai"), and then further
subdivided according to finer and finer distinctions for various
kinds of actions described by the verbs.
And in response to Sergei, I don't see any clear distinction between
commonsense categories as expressed in natural languages and the highly
formalized categories of science, especially mathematics. All of the
scientific terms (including number, space, time, etc.) are refinements
and extensions of the commonsense terms. And the commonsense terms
tend to be much more stable over thousands of years, while the scientific
terms tend to shift their meanings with every passing fad.
John Sowa