Subject: [LC response] To Marco Colombetti
Thank you for your comment
on the OWL 2 Web Ontology Language last call drafts.
The use of the term "Axiom" to mean, roughly, a closed well-formed formula, is now fairly standard in the OWL community. It is also clearly defined. It seems very unlikely that it would cause considerable confusion in those with a sophisticated background in logic, maths, or philosophy, though it may cause some distaste (the way that "ontology" does for some philosophers). Finally, it is deeply embedded in the current documents. Thus, the working group has determined that the alignment would not be worth the costs of fully making the change.
The working group has therefore decided not to make the suggested change in general, i.e. throughout all documents. However, most actual uses of the term "axiom" already refer to "statements that are asserted to be true" (by an ontology) and this use agrees with the general notion of the term in mathematics. We have now updated the OWL 2 Primer to avoid all other uses of "axiom." In particular, there is no more mentioning of "derived axioms" in Section 3. A diff of the changes is given at  and the updated document is at .
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|I suggest abandoning the misuse of term "axiom" to mean
any OWL statement, either assumed as an axiom proper or entailed by an ontology. I see no reason to abandon the classical logical terminology. On the contrary, the use of "axiom" in the document may lead to considerable confusions in all those who have studied logic, abstract mathematics, or philosophy.
I suggest using the term "statement" instead (as usual in all branches of logic). "Axiom" and "theorem" can also be used as in classical logic.
Marco Colombetti Politecnico di Milano