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Re: [ontolog-forum] borrowing terminology (was: [ontology-summit] PLEASE

To: "Conrad Bock" <conrad.bock@xxxxxxxx>
Cc: "[ontolog-forum] " <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Pat Hayes <phayes@xxxxxxx>
Date: Thu, 8 Mar 2007 17:01:51 -0600
Message-id: <p0623091ac2163f04fd3e@[]>
>Ed, et al,
>I'd like to add another effect: disciplines borrowing terms from others
>close to them, but inadvertantly changing the meaning in subtle ways.    (01)

Yes indeed.    (02)

>For example, being a computer scientist, I was shocked to find this on
>the term range":
>   http://en.wikipedia.org/wiki/Range_%28mathematics%29
>At first I thought it was just a folksy effect of the wiki, but the more
>reputable Wolfram site said the same thing:
>   http://mathworld.wolfram.com/Range.html
>So OWL and as the rest of computer science are using "range" a
>nonmathematical way:
>   http://en.wikipedia.org/wiki/Range_%28computer_science%29    (03)

No, wait. There is range-math and range-CS, let 
us agree (although in fact 'range' is used in 
both disciplines in both senses). But the 
OWL/RDFS sense of 'range' is closer to the first, 
mathematical, sense than the second.  The RDFS 
semantics for rdfs:range, also adopted by OWL, is 
that it is a class associated with a function 
(property in W3C-speak) which contains the 
mathematical range and which is contained in the 
mathematical codomain. We were aware of this 
small divergence from standard usage, but to have 
called it rdfs:domainContainer or some such just 
seemed like a losing proposition at the time.    (04)

>Idempotence is another example:
>   http://en.wikipedia.org/wiki/Idempotent
>   http://en.wikipedia.org/wiki/Idempotence_(computer_science)
>    (05)

This isn't a very good example, as these really 
are the same concept, almost word-for-word the 
same definition in fact, but they are applied to 
rather different kinds of application area. But I 
don't think there would be any risk of a 
mathematician seriously misunderstanding what was 
meant here.    (06)

But here's a more serious one. The notion of 
'completeness' of a logic or inference machine is 
well-established in logic, used in virtually all 
textbooks, and has a clear, simple definition. It 
means that if X is a logical theorem then a proof 
of X exists, so that a complete inference engine 
is one which will, in principle, find a proof of 
X (if left to run long enough). But the word has 
been co-opted and given a subtly different 
meaning by a subcommunity of description 
logicians, who are centrally interested in 
decideable logics: for them, it means that an 
engine **will terminate for any input and** will 
yield a proof of X if X is a logical theorem. 
That little **insert** to the standard definition 
has the effect of rendering almost any 
non-description logic system "incomplete" in this 
new meaning of the word. This new meaning has 
been written into the OWL standard (most of which 
was composed by description logicians) so that 
the official W3C specs are now written embodying 
a non-standard sense of a central logical 
concept, one which produces such highly 
misleading (because, when understood standardly, 
false) statements as that OWL-Full has no 
complete reasoning engine.    (07)

>Of course this is just terminology, everyone agrees on the concepts
>involved.  This is where is it critical to have the examples when trying
>to "ontologize" knowledge.  Otherwise, huge debates arise aroung what
>are just terminological differences.    (08)

Agreed. Another example which came up on the 
OWL-1.1 discussion recently was the notion of 
'disjoint union', which has been given a 
non-standard (and genuinely faulty) 
interpretation by formal ontologists, which is 
not in line with its established mathematical 
usage. Another example is the tendency of many 
non-logicians to confuse 'meta' with 
'higher-order', which muddles many debates and 
discussions, especially when precise results 
using one convention are cited in debates which 
use the terminology differently.    (09)

Pat    (010)

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