[CL] Working on a definition of "ontology"

[Ed Barkmeyer]

Pat,

you wrote:

> Bit more than that: this particular terminological nicety has been 
> textbook-standard now for quite a few years, maybe half a century. 

Unfortunately, my formal education is almost that old, 40+ years.

>> But I think too many readers would
>> intuitively expect that the number of variables in a relation is at 
>> least two,
>> especially since John's "conceptual relation" seems to have that 
>> property.

Heather tells me I was wrong in this last.

> Then we need explanatory prose to disabuse them of that idea. :-)

If the term "relation" is the accepted term in the logic world, I don't think 
the readers of CL will have a problem.  It's only us ignorant "computer 
scientists" you have to worry about.  ;-)

>> The upshot of my complaint is that we need a term for that "mathematical
>> structure" that includes both the unary ones and the n-ary ones, and 
>> once upon a time that term was "predicate".
> 
> It was never "predicate". It has been "relation" for 50-odd years or 
> more. 

Good.  That answers my question.  The word is "relation".  Done.

>> And can we say: "A unary relation applied to an 
>> instance/individual is a proposition"?
> 
> You could, though that's not strictly correct in most logics (you get a 
> truthvalue, not a proposition.). We just finished extending CL to IKL, 
> and in IKL a proposition *is* a ZERO-ary relation, see
> http://www.ihmc.us:16080/users/phayes/IKL/GUIDE/GUIDE.html.

To me, a "proposition" is a sentence that is either true or false.  It can be 
proved, disproved, observed, etc., and you get the truth value when you do one 
of those things ("evaluate it").  And I agree that it is zero-ary.  Given the 
"classifier" Person, there is a unary relation Person(?x).  But Person("George 
W. Bush") applies it to an individual, and is zero-ary; it no longer has any 
free variables.  In this case, the truth value is clear.  There are other 
predicates that could be applied to the same individual and engender much 
debate, but they would still be propositions.

>> The reason I care is that I am currently working with another 
>> standards group
>> that is developing "logical formulations" of "unary relations" that 
>> don't have
>> names, and they are very careful to distinguish those from "concepts", 
>> which
>> are "types"/"monadic predicates" that do have names.
> 
> Oh dear, these guys sound to be SERIOUSLY confused. (I wonder why so 
> many people are writing logic standards who know sweet nothing about 
> logic?)

Oh, they are.  (I'm one of them.)  The database and object programming worlds 
have been doing "logic" for years, and now that "semantics" and "logic" is 
getting funding and attention, they want to legitimize what they are doing, 
but not change it, of course.  This group is database logic people and 
computational linguistics people, who are trying to capture the intended logic 
of definitions and rules that are originally expressed in natural language.

The goal is laudable, but the participation is voluntary and variously funded. 
  CL and OWL were lucky in that regard; the modeling world got UML.  It's how 
standards happen.

>>  They lack a term for "unary relation".
> 
> The textbook term, if you want one, is 'property'. Predicates denote 
> properties. Unfortunately, RDF has used "property" to refer to *binary* 
> relations. Sigh.

I rather liked 'property' myself.  I think using that term may unconfuse some 
of the text.  The linguists liked 'characteristic' and then narrowed its use.

>>  The "unary relation" is the "intension" of a set
> 
> What?? That is meaningless. Sets don't have intensions: that is exactly 
> WHY they are sets.

Let me try this a bit more carefully.  In mathematics, it is not uncommon to 
define a "concept" as
   'the set of all x such that <expression involving x>'
Because of all the closed/open world issues that surround database logic, this 
group is very worried about distinguishing the "extension" of the set -- its 
actual members -- from the "intension" of the set -- the rule for membership. 
  So the <expression involving x> is what they mean by the "intension" of the 
set.

To unconfuse many of their definitions, what is needed is a term, which seems 
to be 'property', that means "a function of an arbitrary Thing that returns 
true or false".  The 'property' is monadic, whereas the <expression involving 
x> can involve other variables that are bound within the expression and 
sometimes in the context in which the whole structure appears.  So in a given 
occurrence, the expression resolves to a monadic property.

> This is completely and utterly confused. Not just about terminology: 
> about substance. They sound to have use/mention confusions as well.

It isn't completely and utterly confused, but there is confusion, and it is 
compounded by the terminology.  The problem isn't understanding use/mention; 
it is separating concepts, creating anchor concepts, and writing clear 
definitions, and in some cases, about reconciling the way people say things 
with what they mean.

>> Any recommendations?
> 
> Tell these guys to go and read a logic textbook, or hire someone who 
> has. Seriously: they are just totally off the wall at the moment.

With all due respect, "reading" a logic textbook isn't sufficient.  Read, 
understand, integrate with the views of others who have read the semantics and 
linguistics textbooks, presumably after you have read those, and then 
construct some "ontology" that they can all understand, is what would be 
required, if anyone had the time and funding to do that.

As I said, CL got lucky -- people who knew what to do and how to do it got 
funded.  I've been in the standards business too long to expect most standards 
to be more than useable.  Look at the KIF writeup of about 1992.

-Ed

-- 
Edward J. Barkmeyer                        Email: edbark at nist.gov
National Institute of Standards & Technology
Manufacturing Systems Integration Division
100 Bureau Drive, Stop 8263                Tel: +1 301-975-3528
Gaithersburg, MD 20899-8263                FAX: +1 301-975-4482

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