- From: Jeremy Carroll <jjc@hplb.hpl.hp.com>
- Date: Fri, 06 Jun 2003 18:20:58 +0100
- To: Christopher Welty <welty@us.ibm.com>
- CC: webont <www-webont-wg@w3.org>
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
Received on Friday, 6 June 2003 13:21:22 UTC