[CL] Working on a definition of "ontology"
Heather D. Pfeiffer
hdp at cs.nmsu.edu
Fri Jul 7 17:03:55 CDT 2006
I would not speak for John, but in the CG community a "conceptual
relation" can in fact be unary, i.e. (not). The only real requirement
on a conceptual relation is that it have at least one output; like a
predicate. We do however use propositions as a concept with a single
output. Therefore, John's terminology makes sense.
| Heather D. Pfeiffer | e-mail: hdp at cs.nmsu.edu |
| Computer Science Department | |
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Ed Barkmeyer writes:
> John F. Sowa wrote:
> > The terminology is somewhat variable among different authors,
> > but the most common position is that the word "predicate"
> > refers to the symbol and the word "relation" refers to the
> > mathematical structure that the symbol denotes -- i.e., a
> > predicate is a name of a relation.
> This usage of "predicate" is useful for classification of symbols (which CL
> does not demand), and I agree that it has become common. But the way John
> defines it demands the generalization of "relation" to include the concept
> "unary relation". Viz.:
> > The type labels of conceptual relation nodes can be
> > mapped to and from the predicates of predicate calculus.
> > The type labels of concept nodes can be mapped to and
> > from monadic predicates of an untyped predicate calculus
> > or the types of a typed predicate calculus.
> It follows that monadic predicates must name monadic/unary relations.
> I don't really have a problem with this. (I'm a firm believer in "a rose by
> any other name would smell as sweet".) 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.
> 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". Is it now "relation"? Or shall we look for
> another? And can we say: "A unary relation applied to an instance/individual
> is a proposition"?
> 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. They lack a term for
> "unary relation". The "unary relation" is the "intension" of a set, and the
> "formulation" is the expression/definition of that intension in terms of other
> predicates and "unary relations", which may involve other variables that are
> bound in the context. (This is all about reference to an open set of things
> defined by their relationships to other things.) So it is useful to have a
> term for the unnamed "unary relation" that has the single free variable. Any
> Edward J. Barkmeyer Email: edbark at nist.gov
> National Institute of Standards & Technology
> Manufacturing Systems Integration Division
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