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Re: [ontolog-forum] Summary on language and ontology

To: patrick@xxxxxxxxxxx, "[ontolog-forum] " <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Adam Pease <apease@xxxxxxxxxxxxxxxxxxxxxx>
Date: Tue, 11 Apr 2006 12:09:23 -0700
Message-id: <>
   My thanks to Patrick for persevering with this discussion, and 
taking the time to organize it for everyone's benefit.    (01)

Adam    (02)

At 12:03 PM 4/11/2006, Patrick Durusau wrote:
>Adam Pease and I continued our discussion off-list and we both think 
>that the results of that discussion may be of broader interest.
>I asked Adam to be more specific about what he means by: "meaing is 
>contained in the formal mathematics?"
>The reason I asked that is I was interpreting the "terms," 
>"linguistic names" to be meaningful in and of themselves.
>Adam responded with the following explanation:
>The meaning of '+' has a formal definition (at least thanks to the 
>Principia Mathematica).  The issue of grounding '+' to language or 
>thought is orthogonal to its formal meaning.  The meaning of the 
>arithmetic symbols is no more and no less than their formal 
>mathematical definition.  So it is with terms in a formal ontology.
>If I define
>(instance ?X Human)
>(instance ?X Mammal))
>or in conventional logic notation
>Human(x) -> Mammal(x) ,
>unless I make additional formal statements, this is identical in meaning to
>Foo(x) -> Bar(x)
>The meaning of the terms is not in the linguistic names of the 
>terms, but in its formal mathematical definition.
>What was the "A ha!" moment for me was realizing that Adam meant 
>that in the formal statement Human(x) -> Mammal(x), that Human(x) 
>and Mammal(x) only have the meaning that is defined by the operator, 
>->. The meaning of the terms is defined by the operator in formal statements.
>Granted that with a single formal statement we don't know much, a 
>cumulation of formal statements "define" the terms or linguistic 
>labels. Each part of the complete "definition" of a term is defined 
>by the formal operators in the statements in the ontology.
>Where I was going off-track was in thinking that the terms or 
>linguistic labels had more meaning than was being defined by the 
>formal operator.
>When I posted the foregoing to Adam, he pointed out that defining 
>meaning was not limited to operators. I had just assumed that but he 
>suggested the following to make that clear:
>We're getting very close here.  The only refinement I'd suggest is 
>that it's not just logical operators like '=>', 'and', 'or' etc. 
>that give terms meaning, but also relations and functions, as well 
>as the entire relationship (which includes another or several other terms).
>For example (using SUO-KIF and existing SUMO terms):
>   (instance ?X Head)
>   (part ?Y ?X))
>(exists (?Z)
>   (and
>     (instance ?Z Organism)
>     (part ?Y ?Z))))
>The formal meaning of "Head" is provided by a number of axioms, but 
>even in this axiom, it's not just the logical operators of '=>', 
>'and' and 'exists' that provide that meaning, but the entire 
>statement, including the relationship to "Organism" formed by the 
>entire statement, and the use of the particular SUMO relation "part".
>Note that Adam's original point about the linguistic label "Head" 
>still obtains. The label has no "intrisic" meaning, only formal 
>meaning as defined.
>Hope everyone is having a great day!
>Patrick Durusau
>Chair, V1 - Text Processing: Office and Publishing Systems Interface
>Co-Editor, ISO 13250, Topic Maps -- Reference Model
>Member, Text Encoding Initiative Board of Directors, 2003-2005
>Topic Maps: Human, not artificial, intelligence at work!
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>Shared Files: http://ontolog.cim3.net/file/
>Community Wiki: http://ontolog.cim3.net/wiki/ To Post: 
>mailto:ontolog-forum@xxxxxxxxxxxxxxxx    (03)

Adam Pease
http://www.ontologyportal.org - Free ontologies and tools    (04)

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