Hello All: (01)
This point was quite eloquently made by Drew McDermott in his seminal
technical note (02)
Artificial Intelligence Meets Natural Stupidity (03)
This article makes a very interesting read, and is available at: (04)
http://portal.acm.org/ft_gateway.cfm?id=1045340&type=pdf&coll=GUIDE&dl=GUIDE&CFID=69268953&CFTOKEN=42244022 (05)
Vinay (06)
Adam Pease wrote: (07)
> 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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> (08)
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