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[ontolog-forum] Summary on language and ontology

To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Patrick Durusau <patrick@xxxxxxxxxxx>
Date: Tue, 11 Apr 2006 15:03:15 -0400
Message-id: <443BFD73.5080202@xxxxxxxxxxx>
Greetings!    (01)

Adam Pease and I continued our discussion off-list and we both think 
that the results of that discussion may be of broader interest.    (02)

I asked Adam to be more specific about what he means by: "meaing is 
contained in the formal mathematics?"    (03)

The reason I asked that is I was interpreting the "terms," "linguistic 
names" to be meaningful in and of themselves.    (04)

Adam responded with the following explanation:    (05)

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    (06)

(instance ?X Human)
(instance ?X Mammal))    (07)

or in conventional logic notation    (08)

Human(x) -> Mammal(x) ,    (09)

unless I make additional formal statements, this is identical in meaning to    (010)

Foo(x) -> Bar(x)    (011)

The meaning of the terms is not in the linguistic names of the terms, 
but in its formal mathematical definition.
***    (012)

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.    (013)

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.    (014)

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.    (015)

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:    (016)

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):    (017)

   (instance ?X Head)
   (part ?Y ?X))
 (exists (?Z)
     (instance ?Z Organism)
     (part ?Y ?Z))))    (018)

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".
***    (019)

Note that Adam's original point about the linguistic label "Head" still 
obtains. The label has no "intrisic" meaning, only formal meaning as 
defined.    (020)

Hope everyone is having a great day!    (021)

Patrick    (022)

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    (023)

Topic Maps: Human, not artificial, intelligence at work!     (024)

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