Adam, Patrick, All -- (01)
Yes, indeed, quite a lot of meaning is in the relations (=>, ->, &,
or...) between atomic items in formal notations. (02)
But there's more, much more! (03)
To see this, consider slides 14-17, 35-43, and finally slide 52 of (04)
These slides argue that, if we limit "meaning" to technical notations
(combinations of symbols like =>, ->, &, or..., RDF, URIs...), then
there is no grounding in the world outside the computer. That in turn
severely limits the usefulness of the "meanings" for real world tasks. (06)
Sure, we all know and love our succinct logic and programming notations,
but they were invented before Von Neumann, and they deliberately leave
out the pragmatics of natural language. (07)
That said, full natural language understanding is of course the
"AI-complete problem ". However, there is a minimalist approach that
appears to work, and that does document executably the things that
English sentences mean to people. It's in the implemented system online
at www.reengineeringllc.com, and shared use of the system to write and
run examples via a browser is free. The system functions as a kind of
Wiki for executable English content, and there are already many
ontological and other examples. (08)
Thanks in advance for comments. (09)
-- Adrian Walker (010)
 A reference to NP-completeness, the key open problem for nearly all
of complexity theory. (011)
Internet Business Logic (R)
Executable open vocabulary English
Online at www.reengineeringllc.com
Shared use is free (013)
Reengineering, PO Box 1412, Bristol, CT 06011-1412, USA (014)
Phone 860 583 9677 Mobile 860 830 2085 Fax 860 314 1029 (015)
Adam Pease wrote: (016)
> My thanks to Patrick for persevering with this discussion, and taking
> the time to organize it for everyone's benefit.
> 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
>> 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)
>> (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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> Adam Pease
> http://www.ontologyportal.org - Free ontologies and tools
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