Folks,
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:
>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 (04)
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