Axioms vs. Ontologies?!

"Nicola Guarino" <guarino@ladseb.pd.cnr.it>
Message-id: <guarino.1157083056A@ladseb.ladseb.pd.cnr.it>
Date: Tue, 25 Jul 95 18:03:36 +0000
From: "Nicola Guarino" <guarino@ladseb.pd.cnr.it>
Subject: Axioms vs. Ontologies?!
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John Thompson writes (emphasis is mine):

>Pat Hayes makes some good points about AXIOMS VS. ONTOLOGIES.  But we
>should recognize that the statements in the ONTOLOGY LANGUAGE itself 
>(A is a subtype of B, types C and D have no intersection, E is slot of
>F, etc.) are shorthand for a set of axioms that help define a concept.
> [...]
>So the boundary between the ontology predicates and the additional
>axioms needed is a fluid one, subject to engineering decisions about
>how many predicates to add to the ontology language.  But the
>predicates and the extra axioms are all really axioms that attempt to
>define a concept.

I don't think it is a good idea to *contrast* axioms with ontologies,
assuming that an "ontology language" is just a sort of hierarchy-description
language. Even if you decide to avoid axioms at a first choice just to try
to reach a preliminary agreement at the linguistic level (as Doug Skuce
suggests), sometime during the life-cycle of an ontology you *must* add them
just to exclude unintended interpretations (models) of your ontology: at
this time they are *part* of the ontology (not just "extra stuff"), and
should be suitably expressed by the ontology language. I am very sympathetic
with Pat Hayes in this respect.

Regarding such an "ontology language" (it is the first time I hear this
term), we must distinguish two main purposes, which are somehow related to
the "degree of specification" of a conceptualization by means of a
particular ontology:

- establishing consensus about (the utility of adopting) a particular
ontology among agents who may have different conceptualizations

- describe a set of relevant ontological distinctions and properties to be
shared by agents who already agree on a conceptualization

In the second case, it should be easy to admit that an ontology should
include (relevant) axioms.

In the first case, it may seem that natural language would be enough. I have
tried to show in my recent papers that this is not the case, since even
simple ontological distinctions such as those underlying the different
senses of a word like "red" may be quite hard to describe in a non-ambiguous
way without resorting to formal logical properties. The main purpose of
axioms here is to exclude unintended models. The problem is that the
ontological language used to state such "consensus-establishing axioms" may
need to be *richer* than the one used in the case of a mutually agreed
underlying conceptualization. However, in this case it is not a matter of
"engineering decisions", since these axioms needs to be understood by
humans, not by computers as in the second case.

In conclusion, axioms are *part* of an ontology; the taxonomy (or its
corresponding axioms) is of course another (essential) part, as Fritz
Lehmann underlines. I would add however that the fact that an ontology may
be described by a bunch of axioms doesn't mean that an ontology is *just* a
logical theory, as Pat Hayes stated some time ago: it is a logical theory
*of a particular kind*, and its main property lies in the fact that each of
its formulas is *necessarily true*. A more elaborate discussion of these
ideas can be find in the paper submitted for the discussion at the next
IJCAI workshop (which is the same as the one presented at the KB&KS
conference in Twente last Spring: "Ontologies and Knowledge Bases: Towards a
Terminological Clarification", accessible on
http://www.ladseb.pd.cnr.it/infor/Papers/OntologyPapers.html).

Cheers

-- Nicola