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Re: [ontolog-forum] Conceptual Schema, ISO TR9007 (1987) and Ontology

To: Sjir Nijssen <sjir.nijssen@xxxxxxxxxxxx>
Cc: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Edward Barkmeyer <edward.barkmeyer@xxxxxxxx>
Date: Wed, 05 Jan 2011 13:02:39 -0500
Message-id: <4D24B23F.8030309@xxxxxxxx>
Sjir,    (01)

I think we have an important difference in terminology.    (02)

Sjir wrote this definition (from TR9007):    (03)

> *Conceptual schema*
> *A consistent collection of sentences expressing the necessary 
> propositions *
> *that hold for a universe of discourse.
> *
>    (04)

Given that definition, I would write:    (05)

Ontology:  A consistent collection of sentences expressing propositions 
that hold for a universe of discourse in a language supported by 
automated reasoning tools.    (06)

The distinction between 'necessary proposition that holds' and 
'proposition that holds' is an alethic or non-monotonic logic concern.  
One can argue that it distinguishes propositions that hold for more than 
one domain of discourse, which is, of course, a critical concern for 
database technologies.  And in fact, this is a critical point.  
Non-monotonic behavior is part of the interpretation given to conceptual 
schemas by the automated reasoning tools that support the language.    (07)

An ontology consists of a set of asserted propositions and an 
interpretation that is based on the language used.
The same is true of a conceptual schema, but the importance of language 
and its interpretation was overlooked in TR9007.    (08)

So, a conceptual schema is a kind of ontology.  A set of propositions 
formulated in a description logic language is a different kind of 
ontology.  And a set of propositions formulated in an FOL is a third 
kind of ontology.  The constraint on the language -- "supported by 
automated reasoning tools" -- constrains the propositions that can be 
formulated in important ways.  The question is:  What is the difference 
between the set of propositions that can be formulated in a "conceptual 
schema" language like ORM, and the set of propositions that can be 
formulated in a DL language or an FOL language?  And what is the 
consequence for the intended applications of the ontology?    (09)

We know that DL semantics is a proper subset of FOL semantics, and thus 
every DL model has an FOL cognate.  Unfortunately, the semantics of 
conceptual schema languages and the semantics of FOL languages are 
significantly different in ways that make it hard to construct an FOL 
ontology from a conceptual schema, and impossible (I think) to construct 
an arbitrary FOL ontology in a conceptual schema language.    (010)

So, having resolved the definition issue, our task is to distinguish the 
kinds of statements that characterize business situations and practices 
into those that can and cannot be expressed in languages with these 
different semantic interpretations.     (011)

Sjir, are we to take Terry Halpin's thesis as the reference semantics 
for a typical conceptual schema language?  Did ISO TR9007 take into 
account other conceptual schema languages (e.g., SQL) that have a 
different reference semantics?  It would be nice to have a reference 
specification for the fruit we are comparing to DL or FOL apples.    (012)

-Ed    (013)

Edward J. Barkmeyer                        Email: edbark@xxxxxxxx
National Institute of Standards & Technology
Manufacturing Systems Integration Division
100 Bureau Drive, Stop 8263                Tel: +1 301-975-3528
Gaithersburg, MD 20899-8263                Cel: +1 240-672-5800    (014)

"The opinions expressed above do not reflect consensus of NIST, 
 and have not been reviewed by any Government authority."    (015)

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