Re: D7 - Which languages are better than OWL?
Philippe, Gian Piero, and Stavros,
A few comments.
> in 2007, no W3C_language provides a way to specify in a concept
> definition that some relations are mandatory.
The words 'mandatory' and 'optional' in some KR languages are
usually synonyms for the words 'necessary' and 'possible',
which are the common terms in modal logics.
However, it is important to note that a KR language can have a
modal effect by the way it is *used* even if there are no modal
words or operators in the language itself.
People in the description logic community, for example, often
make the claim that DLs express necessary conditions on the
concepts or terminology that is being defined and that the
information in a database (or other repository of assertions)
expresses information that is merely contingently true.
That effect is not obtained by any operators in the DL statements,
but by treating the DL ontology as having greater *entrenchment*
than the assertions in the database. Some older terms are T-box
(terminology box) for the DL statements as opposed to the A-box
(assertion box) for the ordinary facts in the database. That
modal effect is explained by Dunn's semantics for modal logic:
1. Distinguish two kinds of true statements, called laws and
facts.
2. Anything provable from the laws is necessarily true, and
anything consistent with the laws is defined to be possible.
3. In a normal modal logic (ordinary modes of necessary and
possible), the laws must be a subset of the facts. But in
a nonnormal modal logic (e.g., deontic modes of obligatory
and permissible), some laws might be violated (e.g., because
people are sinners).
Michael Dunn showed that this semantics is equivalent to Kripke's
semantics in terms of possible worlds. For KR languages, however,
Dunn's semantics has a more natural interpretation (and implementation)
in terms of databases and knowledge bases. Database constraints, for
example, are treated as laws, and the stored data is merely contingent.
For a brief summary of Dunn's semantics (with references), see
Section 2 of the following paper:
http://www.jfsowa.com/pubs/laws.htm
Laws, Facts, and Contexts
In short, statements in any notation for logic can have a modal effect
by assuming that a certain collection of statements has a greater
degree of entrenchment than another collection. The modal effect does
not arise from any differences in the notation, but from differences
in the assumed level of entrenchment.
SM> Lakoff has pointed out the centrality of metaphor, analogy, and
> graded categories in natural language, contrasting them with the
> property-based strict categories of Aristotle.
Lakoff's examples would not have caused any problem for Aristotle,
who had defined modal syllogisms for reasoning about categories
with necessary and possible properties. Aristotle also made the
point that in empirical subjects (such as biology, which was the
science to which he had devoted the greatest attention) strict
top-down definitions are not as useful as bottom-up analyses of
the data. And Aristotle did some very good work in analyzing
metaphor in the his book _Poetics_.
People often contrast Aristotle's definitions by genus and differentiae
with definitions by prototype, but Aristotle discussed the advantages
and disadvantages of both. For biology, he was very careful about
starting with the data. One of his best-known examples was his study
of the embryo by starting with 30 chicken eggs and breaking open one
egg each day in order to analyze and describe the development.
Although I have a great deal of sympathy with many of Lakoff's
positions, his sweeping generalizations of what other people said
are rarely based on a careful analysis of the data. Following is
a review I wrote about another of his books:
http://www.jfsowa.com/pubs/lakoff.htm
Review of Lakoff & Johnson, _Philosophy in the Flesh_
And by the way, Mark Johnson is usually a more careful writer, and
I would blame Lakoff for the overgeneralizations in this book.
SM> How to treat these in an ontology?
I would never recommend a single monolithic ontology for everything,
and I've been proposing an organized collection of task-oriented
ontologies for all the special cases. Following is a statement
of the problem:
http://www.jfsowa.com/pubs/challenge.pdf
The Challenge of Knowledge Soup
I also have some suggestions for the solution, but that's a topic
for a much longer thread.
John Sowa