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## [ontolog-forum] Summary on language and ontology

 To: "[ontolog-forum]" Patrick Durusau Tue, 11 Apr 2006 15:03:15 -0400 <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) (=> (and (instance ?X Head) (part ?Y ?X)) (exists (?Z) (and (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 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    (023) Topic Maps: Human, not artificial, intelligence at work!    (024) _________________________________________________________________ Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/ Subscribe/Unsubscribe/Config: http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/ Shared Files: http://ontolog.cim3.net/file/ Community Wiki: http://ontolog.cim3.net/wiki/ To Post: mailto:ontolog-forum@xxxxxxxxxxxxxxxx    (025) ```
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