You and I share enough mails off-line for me to know that if you just wanted the answer, you'd ask me off-line. So, in fear of being led around by socratic method, let me flip this in a way that only an Aussie would and say that because I started this thread...I kinda get to be the one to play Socrates.
In reading your response in leiu of a thank you, I remain a little unconvinced. i.e. If you know enough about isomorphism, you wouldn't need an example.
I am sure that you would agree that it is one thing to read of Champollion and another to understand what he did, it is one thing to read of Turin cracking the enigma code and it is another thing to understand how he did it, it is one thing to apprecate that two geometric shapes have the same area...and another entirely to understand the reason 'why'.
I am not the teacher Brian, so I will only offer this by way of quote to the Gospel of Thomas:
"Whoever has ears to hear, let him hear." (Gospel of Thomas, 8)
1. When you perform 45432454509 * 13452356727 on paper in pencil, do you consider your 'working' in the answer, or do you consider 611173585038267632043 (the answer)?
The answer to that is the answer to your question.
2. When you consider '611173585038267632043' as a 'message', then '45432454509 * 13452356727' is a valid 'interpretation' of that message.
3. The following is a theorem in ORM and a set of 'theorems' in KL. A 'proof' is a set of theorems. As a hint, please note that nORMa is smart enough to tell that something is up, and raises a little red flag (see picture).
NB For the student: Has nORMa interpreted the 'message'? If so, what does that 'interpretation' look like when you write it in KL? If you were to take that interpretation in KL and draw it as an ORM diagram....what would it look like?
It is worth noting that there are PHDs who would argue that you can't do proofs in ORM. The following are quotes from PHDs.... and it is worth nothing that they are the same ones reading and assessing your (the audience) papers for the ORM conference. There's nothing person there, because I don't know who they are.
Before I provide them...let me repeat the message "Whoever has ears to hear, let him hear".....
A warning...the following may be hard to take for lovers of ORM, Godel and Proof Theory...
"the fact that in ORM one can only represent facts, whereas in theories like KL and PM one not only represents facts but also the PROOFS of properties of facts."
"One could also say that KL is complemenetary to ORM in the sense that ORM provides the facilities to represent facts, whereas KL offers the extra facility to also REASON about these facts."
"KL offers deduction rules (a la Gentzen, and/or semantic tableaus a la Beth) and provides facilities to actually do proofs about properties of ORM models. You do the proofs in KL, and not in ORM."
"In [formal theories like KL and PM] you also do the actual proofs (of, e.g. the property 1+1 = 2) [,you can't do proofs in ORM]"
"Godel introduced an ingenious coding of not only facts but also proofs of properties of facts as numbers in number theory. [you can't do isomorphic proofs in ORM]"
"Inspection of [an ORM diagram] shows no representation of logic (in the sense of deduction rules and proofs), hence an important part of a formal system a la KL [..] is lacking."
"the main reason for introducing KL was the additional facility to REASON about properties of ORM models in a formal setting.'
[The proof above in KL is] obviously [..] an intensional proof of contradiction [..] and at least verifiably correct and complete) while the "Population Table" [(in the ORM diagram above)] is unnecessary and therefore confusing extensional interpretation. It does not [provide an isomorphic interpretation of the theorems of KL] but at most -trivially!- "illustrates" the proof for people not able to read [KL].
I'll leave it there Brian. I remain yours,