Ali and Pat, (01)
I agree with Pat's comments on this topic, but I'd like to
add a few. (02)
Nicola G> This set of assumptions has usually the form of a
> first-order logical theory, where vocabulary words appear as
> unary or binary predicate names, respectively called concepts
> and relations. (03)
AH> Though i'm not sure why vocabulary words are restricted to
> unary or binary predicate names (04)
PH> Me neither. Writing in 2008, Nicola was probably intending to
> make a nod at the prevailing widespread use of description
> logics, which are restricted to the unary/binary case. (05)
As an example, the English word 'add' maps to the mathematical '+',
which represents a function with two inputs and one output. (06)
It is possible to represent such things with a concept type Add
that represents an add operation, which is linked to three dyadic
relations: (07)
1. Arg1 links the Add concept to the first argument. (08)
2. Arg2 links Add to the second argument. (09)
3. Rslt links Add to the result. (010)
PH> In practice, there seems to far more unary/binary than anything
> else, and one can routinely encode an n-ary relation is a
> conjunction of binary ones. (011)
Yes. And it's desirable to use a logic that can relate the different
representations by if-then rules, such as (012)
(forall (x y z w)
(if (and (Add w) (Arg1 w x) (Arg2 w y) (Rslt w z))
(= z (Sum x y)) )) (013)
PH> Most ontologies are built on a skeleton of taxonomy, or at least
> a subclass hierarchy. Its hard to avoid having such a structure
> somewhere in any large ontology, in fact. (014)
Yes. That has been common practice since Aristotle. In fact, many
of the ontologies that are written in OWL don't use anything beyond
Aristotle's subset. (015)
John Sowa (016)
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