Ontology Definition Redux

I just had a debate with an ontologist friend about whether or not an ontology is a kind of a taxonomy and a taxonomy is a kind of controlled vocabulary.

I believe what is true in Formal Concept Analysis should be true in every ontology: every generalization must have fewer attributes than its specializations, and every specialization must have more attributes than its generalizations.

If we were to create an ontology about controlled vocabularies, taxonomies, and ontologies, we would say that a controlled vocabulary is a set of words; a taxonomy is a set of terms with hypernym, hyponym, and synonym relations between the terms; and an ontology is a set of terms with hypernym, hyponym, and synonym relations between the terms, with additional relations and perhaps axioms. Therefore, I think an ontology is a kind of a taxonomy and a taxonomy is a kind of controlled vocabulary.

What do you think?

Here is more supporting evidence I've dug up:

• CLARITY IN THE USAGE OF THE TERMS ONTOLOGY, TAXONOMY AND CLASSIFICATION: "A very simple ontology could perhaps better be named 'taxonomy'"
  
• What are the differences between a vocabulary, a taxonomy, a thesaurus, an ontology, and a meta-model?:
• "A controlled vocabulary is a list of terms that have been enumerated explicitly. This list is controlled by and is available from a controlled vocabulary registration authority. All terms in a controlled vocabulary should have an unambiguous, non-redundant definition."
• "A taxonomy is a collection of controlled vocabulary terms organized into a hierarchical structure."
• "A formal ontology is a controlled vocabulary expressed in an ontology representation language."
• "The word 'ontology' has been used to refer to all of the above things."
• Ontology Development 101: A Guide to Creating Your First Ontology:
  
• "The ontologies on the Web range from large taxonomies categorizing Web sites (such as on Yahoo!) to categorizations of products for sale and their features (such as on Amazon.com)."
• Organizing Knowledge with Ontologies and Taxonomies:
• "The concepts are defined in an ontology that maps the main ideas and their relationships. It also include the creation of a set of terms that defines how to label items according to the concepts described in the conceptual map. This structured set of terms is a taxonomy."
• "Taxonomies are the classification scheme used to categorize a set of information items. They represent an agreed vocabulary of topics arranged around a particular theme."
• Building and Using Ontologies
• "An ontology may take a variety of forms, but necessarily it will include a vocabulary of terms, and some specification of their meaning."