Re: [ontolog-forum] Constructs, primitives, terms

[Amanda Vizedom <amanda.vizedom@xxxxxxxxx>]

Pat +1!

If they are logically inconsistent, they are not the same "term" where "term" = conceptual/ontological item.

Systems A and B may use the same "term" where "term" = lexical item, to express different concepts. That's not a logical inconsistency. It's an ordinary difference in language (natural or artificial), and can be handled well by mapping those lexical expressions to different concepts.

-Amanda

P.s.: My controversial stand regarding labels grows in part out of the frequency and ordinariness of this situation. It's much harder for humans to do this mapping quickly and correctly when, say, Systems A and B use *lexicial* term "gruefulit" and some concept in the ontology ont1 is named "ont1:gruefulit."  This exerts a strong cognitive pull towards mapping the lexical items SystemA-"grufulit" and SystemB-"gruefulit" to "ont1:grufulit." Since Systems A and B use lexical item "gruefulit" to express different concepts, if they are both mapped to ont1:gruefulit, that *will* be inconsistent. And mapping one but not the other to ont1:gruefulit makes thinks more confusing and harder to parse intuitively.

For this kind of usage, better accuracy and intuitiveness come from calling a concept ont1:0395 (some existing label), and deciding based on meaning whether it should also have labels ("gruefulit", sysA) or ("gruefulit", sysB) or neither. 

On Fri, Mar 2, 2012 at 00:38, Patrick Cassidy <pat@xxxxxxxxx> wrote:

John,
 I am curious to know what kinds of inconsistency you are referring to:

>  So far, so good.  But a problem arises when systems A and B
>  exchange messages that use only the "common" vocabulary defined
>   by the shared URIs.  They may use the same terms, but their
>  specialized "senses" of the terms may be inconsistent.

  Does this refer to cases where two communicating systems define (or
otherwise logically specify the intended meaning) of the *same* term (e.g.
'widget'), but use different definitions?  Of course, they may be logically
inconsistent.  But don't the two terms have different URI's (assuming the
URIs depend on the originating system)?
  In the interoperability scenario I have assumed that the mediating system
that provides a translation of local systems depending on a common
conceptual defining vocabulary would have to check for identity of
definitions not in the common vocabulary, and *not* assign identity to two
terms that do not have identical definitions, regardless of what local term
is used to label that ontology construct.

Pat


Patrick Cassidy
MICRA Inc.
cassidy@xxxxxxxxx
908-561-3416

-----Original Message-----
From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx
[mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of John F. Sowa
Sent: Thursday, March 01, 2012 10:17 AM
To: ontolog-forum@xxxxxxxxxxxxxxxx
Subject: Re: [ontolog-forum] Constructs, primitives, terms

Dear Matthew, Chris, and Nicola,

MW
> One of the problems with primitives is that if you are developing
> an ontology, then it is quite likely that entities that start out
> primitive may acquire a complete definition over time.

Yes, indeed.  That is also a problem with URIs that are supposed to
point to unique definitions.  When you import such a definition into
a context A that contains a lot of other axioms and definitions, the
simple imported terms will be used in more specialized ways.

Then if somebody else imports the same term into a different context B
with different axioms (or procedures), it will be used in a different
specialization.

So far, so good.  But a problem arises when systems A and B exchange
messages that use only the "common" vocabulary defined by the shared
URIs.  They may use the same terms, but their specialized "senses"
of the terms may be inconsistent.

CM
> It is impossible to define addition in terms of zero and successor.
> The reason for this, in a nutshell, is that the addition symbol is
> not eliminable; given the axioms for addition along with the axioms
> for zero and successor, you can "say" things that you cannot say
> in terms of the axioms for zero and successor alone...

Yes.  In general, a "closed form" definition can be eliminated.
For example,

   f(x) =  3x^2 + 5x - 17

You can replace any occurrence of f(y) by replacing x with y in the
defining _expression_.  But you can't do that for functions that are
directly or indirectly defined by recursion.  That is true of most
terms in any realistic ontology.

You can adopt a language that prohibits recursion, but that doesn't
solve the problem.  It just makes it impossible to state the full
definition of your critical terms.

Basic contradiction:  You can't have a practical system with completely
specified URIs and a restricted language to define them.

NG
> This is the reason why lightweight ontologies work very well as long as
> their terms are simple and understood by everybody. When we have very
> general, highly ambiguous terms, or technical terms whose meaning is
> not understood by everybody, then the importance of a clear semantic
> characterization (i.e., an axiomatic ontology) increases.

Yes, indeed.  And as in the examples by Chris, those axioms will be
explicitly or implicitly recursive.

The net result (Horror of Horrors!) is that your ontology language
will be undecidable.  But as anybody who has worked with any practical
application knows, people have learned how to use undecidable languages
in practical ways for real-world applications.  In fact, decidable
languages are *never* used in practical applications without having
undecidable supplementary languages to do all the "heavy lifting".

John

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