Re: representation and replacement

In article <M5fae.1559$pk5.1255@fed1read02>, "vsgdp" <spam@xxxxxxxx> wrote:

>Okay, suppose you have two objects, where one object A represents the other
>object B, and you can always obtain one object from the other.
>
>I would like to write A = B (to do replacements), but technically, they are
>not of the same type, so it doesn't seem like you can really say they are
>equal unless you accept the abuse of notation.
>
>I though of using the logical equivalence symbol, but these are objects and
>not truth statements.
>
>What should I do?

Maybe try axiomatizing the behaviour that you want "represents" to have.
For example, let rep(a,b) mean that a "represents" b. With only that, it's
an undefined notion; so then construct appropriate axioms to define it. For
example, you appear to want various axioms of replacement:
Aa Ab (phi(b) ^ rep(a,b) -> phi(a))
where phi(x) is any first-order formula with 1 free variable x.

What other properties do you want "represents" to have?

--
---------------------------
| BBB b \ Barbara at LivingHistory stop co stop uk
| B B aa rrr b |
| BBB a a r bbb | Quidquid latine dictum sit,
| B B a a r b b | altum viditur.
| BBB aa a r bbb |
-----------------------------
.

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