Re: WOWG: Report from WWW 2003 - OWL presentation/issues

Jeremy,

100% agreement - the "normal" discussion about triples is, as I think you 
imply by using "normal", the one most people use and assume.   And this 
appears second order to most people since it allows you to predicate a 
predicate.   However, as you point out, there is a mapping to a 
first-order system.    This is why I claimed it has a higher order syntax, 
but not a higher-order semantics.

I agree, btw, with Peter that the mapping to first order is NOT trivial, 
though I may be less skeptical that he is that it is correct.

-Chris


Dr. Christopher A. Welty, Knowledge Structures Group
IBM Watson Research Center, 19 Skyline Dr., Hawthorne, NY  10532     USA   
 
Voice: +1 914.784.7055,  IBM T/L: 863.7055, Fax: +1 914.784.6912
Email: welty@us.ibm.com, Web: http://www.research.ibm.com/people/w/welty/




Jeremy Carroll <jjc@hplb.hpl.hp.com>
06/06/2003 01:20 PM
 
        To:     Christopher Welty/Watson/IBM@IBMUS
        cc:     webont <www-webont-wg@w3.org>
        Subject:        Re: WOWG: Report from WWW 2003 - OWL 
presentation/issues


Sorry for not replying sooner ...

Christopher Welty wrote:

> 
> Jeremy,
> 
> I've argued this with Pat several times.  I'd like to see an 
> authoritative definition of what "first-order" means, otherwise we're 
> all using our own definitions.  In any dictionary of logic or philosophy 

> or mathematics that I've been able to find, "first-order" is defined as 
> "not higher order" and "higer order" is defined as predication of 
> predicates (or functions of functions).
> 
> Until someone produces an authoritative definition of first-order that 
> says something else, I don't think it's ever "simply incorrect" to call 
> RDFS higher-order. 


I see what you're getting at.
The normal discussion about triples is to call the middle term a 
predicate, 
and then RDF permits predicates to apply to predicates.

However, a different understanding of RDF; for examle that seen in the 
DAML+OIL axciomatic semantics use essential one 3 place predicate for 
expressing a true triple.

So - in terms of underlying complexity and difficulty a first order theory 

is one that can be mapped into first order logic; and RDFS trivially can 
be. Truely higher order statements like Grelling's paradox[1] cannot be 
expressed in RDF.

Jeremy

[1]
[[
If an adjective truly describes itself, call it "autological", otherwise 
call it "heterological". For example, "polysyllabic" and "English" are 
autological, while "monosyllabic" and "pulchritudinous" are heterological. 

Is "heterological" heterological? If it is, then it isn't; if it isn't, 
then it is. Grelling's paradox cannot be expressed in first-order 
predicate 
logic, and is difficult to prevent in higher-order predicate logics.
]]
http://www.earlham.edu/~peters/courses/logsys/glossary.htm#g