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[ontolog-forum] Ontology mapping & "theorems for free"

To: ontolog-forum@xxxxxxxxxxxxxxxx
From: Nicolas F Rouquette <nicolas.rouquette@xxxxxxxxxxxx>
Date: Fri, 10 Dec 2004 10:50:04 -0800
Message-id: <41B9EFDC.60902@xxxxxxxxxxxx>
Has anybody noticed a strong kindship between the issues we face in 
modular / formal ontology development
relative to issues of mapping and the ideas of Galois connections & 
"theorems for free" ?    (01)

While I was listening to Mark Musen's presentation,    (02)

http://ontolog.cim3.net/cgi-bin/wiki.pl/wiki.pl?ConferenceCall_2004_12_09    (03)

I started to think about how good software engineering practices solve 
some of the
problems of ontology development such as those Mark mentioned in the context
of NCI's change management process.    (04)

The issues there are about dealing with the distributed changes to 
various parts
of an ontology or to several ontologies that are used in diverse 
The problems stem from the fact that we can never anticipate all possible
ways in which somone is going to use an ontology or depend on several 
The changes made can affect such users and break the logical foundations 
need for whatever reasoning tasks they do (classification, subsumption, 
query, optimization, compilation, ...)    (05)

 From a software point of view, it seems that ontology development lacks
a precise way to talk about software engineering notions like scope, 
dependencies, extension points, .... I know that there's a lot of work 
in ontology
with the notion of "topic map" and "concept map"; I don't know enough about
that line of work to tell if the issues they have looked into adress all 
of the
software engineering concerns of distributed change management.    (06)

There is an alternative approach to change management with the idea
of using category theory, Galois connections and theorems for free as
a heavy-duty machinery to "proove" that the consequences of changes
made in an ontology wouldn't break properties we need in uses of that 
ontology.    (07)

This alternative approach is based on a paper I read from Kevin and 
Roland Backhouse:    (08)

http://portal.acm.org/citation.cfm?id=1007979    (09)

Kevin and Roland show an application of theorems for free and Galois 
in order to "proove" statements (safe abstract interpretations)
about a set of things (implementation level) in terms of logical 
properties about
functions and the way they are used to build an implementation (this is 
where I understand
we need to have a parametric and higher-order capability to talk about 
functions and about their application)    (010)

I wish that I could fully understand Kevin and Roland's paper.
Alas, I was raised in France, not Britain; but the more I attempt
to understand their paper, the greener British grass looks to me.    (011)

Seriously though, we can take a step back and see:    (012)

- OWL made a number of tradeoffs biased towards practicality.
- the field of abstract interpretation, etc... offers a number of 
interesting ways
  to get help from formal specifications
- an ontology is a formal specification of some kind    (013)

The connection here seems to me that:    (014)

- the DL formulas we use in an ontology stand for the functions that 
Kevin and Roland use to talk about abstract specifications    (015)

(e.g the x operator introduced in their running example on p. 2)    (016)

- the "fold" function stands for a specific kind of logical inference 
like classification, subsumption, etc..    (017)

(e.g., the concept of "defined class" in Protege/OWL)    (018)

Is this just a French/British cultural joke or is there something worth 
pursuing here?    (019)

My hunch is that theorems-for-free says: "here's a way to put a theorem 
proover to a practical use for ontology
development to answer some practical questions in a different way than 
is currently done or not done at all,
e.g.: upper/lower ontology consistency; compatibility of multiple upper 
ontology mixins.    (020)

If these comments make sense to you, I'd be very interested to read your 
opinions/feedback/suggestions about them.    (021)

-- Nicolas.    (022)

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