Re: SUO: KIF syntax and semantics and a basic ontology
Pat and Robert,
Your discussion reminds me of a point that I believe we should
highlight in the tutorials or commentary about the methodology
for developing ontologies (or any formal theory of any kind).
>Again, I would say not, in general. The basic point is that it is
>impossible to say that a particular ontology *completely defines* the
>meaning of a symbol. If we could say in some sharp way that A
>completely defined the meaning of r, while B and C only used that
>meaning, then I would agree that it would be otiose to insist on
>distinguishing b1#ai#r from b2#a2#r; but I don't really beieve this
>ever happens; and certainly there is no model-theoretic basis for
>every saying such a thing, since every assertion made using 'r' adds
>some component of meaning to it by restricting its possible
>interpretetions in some way...
I agree. But we should include a comment about different kinds
of definitions. I suggest some discussion and examples, such as
1. Closed-form definitions that define one symbol or
expression as an exact synonym for another; e.g.,
f = (lambda x,y)(2xy -17)
2. Axiomatic specifications in which some symbol is
introduced as a new primitive that participates
in certain relationships with other incompletely
defined primitives; e.g.,
Monadic predicats: dog, cat, animal.
Axioms:
(Ax)(dog(x) -> animal(x))
(Ax)(cat(x) -> animal(x))
~(Ex)(dog(x) & cat(x))
These three axioms tell us that cats and dogs are animals
and nothing is both a cat and a dog. But the meaning of
these three predicates will continue to be specified in
more detail as new axioms are imported from other modules.
>Another possibility is to allow an ontology to import another one
>without any prefixing. If this option were generally used, of course,
>all these identities would be automatic. There would however be a
>great danger of inadvertent inconsistencies appearing.
Sometimes we want to do that. As in the example about cats
and dogs, we may want to import information about them from
many different sources in order to get a fuller picture of
what it means to be a cat or a dog.
John