[CL] Working on a definition of "ontology"

[Ed Barkmeyer]

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 
recommendations?

-Ed


-- 
Edward J. Barkmeyer                        Email: edbark at nist.gov
National Institute of Standards & Technology
Manufacturing Systems Integration Division
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