Re: A statement on dbdebunk.

Keith H Duggar wrote:
> Erwin wrote:
> > "My material is sound because unlike all the stuff
> > floating in the industry, the logical level is formal and
> > the conceptual level was developed to allow 1:1 mapping to
> > it.
> >
> > Conceptual model: informal business concepts
> > (enterprise-specific)
> >
> > Logical model: formal representation (as much semantics as
> > a system is capable of "understanding")
> > (enterprise-specific)"
> >
> > Conceptual model === INFORMAL
> > Logical model === FORMAL
> > Conceptual model "ALLOWS A 1:1 MAPPING" to the logical
> > model
>
> Note also that "as much semantics as a sytems is capable of
> 'understanding'". That confirms that
>
> > Now, it seems to me that "allows a 1:1 mapping" means that
> > there is some kind of isomorphism between the things that
> > are mapped in such way.
>
> He did not mean (nor did he state) isomorphism. He stated
> the mapping is 1:1. Remember that isomorphism is 1:1 /and
> ONTO/. The mapping is not onto. He seems to say that there
> are conceptual elements that are not mapped to the logical
> model.

Shouldn't that be, "He seems to say that there logical elements to which no conceptual elements map."?
>
> > And the fact that some kind of isomorphism between two
> > things can be found, implies that any quality or property
> > that holds/exists/is proven for either of the things
> > mapped, necessarily also holds/exists for the other thing
> > mapped.
> >
> > So if model X has the property of being formal in some
> > sense, and model Y is in some way isomorphic to model X,
> > then it necessarily follows that model Y is also formal in
> > that same sense as model X is formal .
> >
> > So the statements quoted here, seem contradictory to me,
> > if not quackery.
> >
> > Anyone care to correct me on this, or comment in any other
> > way?
>
> You assumed isomorphism and reached a contradiction. Your
> premise was simply false. At least it appears so given the
> excerpt.
>
> Does this clear it up or am I missing something too?
>
> -- Keith -- Fraud 6

To (hopefully) clarify: Consider the set of conceptual elements C = {C1, C2, C3} and logical elements L = {L1, L2, L3, L4}. The following mapping from C to L is a 1-to-1 mapping: {C1, L1}, {C2, L2}, {C3, L4}
yet, it is not ONTO and certainly doesn't establish isomorphism. Received on Mon Aug 21 2006 - 21:01:01 CEST