Re: Object identity


Gabriel Claramunt wrote:
What is not an interpretation? Note that an interpretation, formally
defined as a mathematical function, is the standard way to deal with
the relationship between model and what is modelled. I've seen it in
texts on mathematical logic, automated theorem proving, relational
modelling etc.

A small comment: formally, your "Interpretation" cannot be a mathematical
function, because in your definition you could have: I(a)=X and I(a)=Y with
X<>Y.

An interpretation is a function by definition. Domain = some specified
set of values or objects that are stored in computer memory. Codomain
= some specified set of entities in the problem space.

Yes a mathematical function can't have I(a)=X and I(a)=Y with
X<>Y. But why do you think my definition allows that? I said it was
a function so therefore that can't happen.


So, formally, either your function I doesn't exists or the statement "I(x) =
I(y) => x = y" is true....and you're saying that Interpretation as a
function exists... now I'm confused about the point you're trying to
prove...

The statement "I(x) = I(y) => x = y" is just the formal definition
of 1-1. Take a look at "Injective function" in Wikipedia.


Cheers,
David Barrett-Lennard

.