Hello to all of you.
There is also the model-theoretic side of
this discussion. As an example see: (01)
http://plato.stanford.edu/entries/model-theory/ (02)
Regards, (03)
-Arturo (04)
On Tue, 11 Apr 2006, Vinay K. Chaudhri wrote: (05)
>
> Hello All:
>
> This point was quite eloquently made by Drew McDermott in his seminal
> technical note
>
> Artificial Intelligence Meets Natural Stupidity
>
> This article makes a very interesting read, and is available at:
>
>
>http://portal.acm.org/ft_gateway.cfm?id=1045340&type=pdf&coll=GUIDE&dl=GUIDE&CFID=69268953&CFTOKEN=42244022
>
> Vinay
>
>
>
> Adam Pease wrote:
>
>> Folks,
>> My thanks to Patrick for persevering with this discussion, and taking
>> the time to organize it for everyone's benefit.
>>
>> Adam
>>
>> At 12:03 PM 4/11/2006, Patrick Durusau wrote:
>>
>>> Greetings!
>>>
>>> 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):
>>>
>>> (=>
>>> (and
>>> (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
>>>
>>> --
>>> Patrick Durusau
>>> Patrick@xxxxxxxxxxx
>>> 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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>>
>>
>> ----------------------------
>> Adam Pease
>> http://www.ontologyportal.org - Free ontologies and tools
>>
>>
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> (06)
==============================================================
Arturo Sanchez, PhD e-mail: asanchez@xxxxxxx,
Associate Professor arturo@xxxxxxx
University of North Florida Phone: (904) 620-1314 (of)
CIS Department
4567 St. Johns Bluff Rd, South Fax: (904) 620-2988
Jacksonville, FL 32224-2669 http://www.unf.edu/~asanchez
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