Re: POOD and the Unique Name Assumption

From: Marshall <marshall.spight_at_gmail.com>
Date: Sat, 14 Jun 2008 00:25:14 -0700 (PDT)
Message-ID: <ae8d562e-884d-41cf-bab6-993d773b127a@u12g2000prd.googlegroups.com>


On Jun 12, 4:21 am, "Brian Selzer" <br..._at_selzer-software.com> wrote:
>
> >>>>I guess I don't really know what this "Unique Name Assumption" is.
>
> >>>The Unique Name Assumption ensures that whenever two names are different,
> >>>the objects they represent must also be different.
>
> >> What is motivation for such an assumption? It doesn't seem to hold in
> >> any formal system I can think of.
>
> The unique name assumption is concerned with how first order language
> elements are mapped to objects in the Universe of Discourse. How could
> forcing that mapping to be bijective cause aliasing errors?

Well, to be pedantic (and who doesn't love an opportunity for that?) I'd
have to say here we're talking about *anti* aliasing errors.

You said specifically "language elements." So that definitely means things
like variable names, and not values from the domain of discourse. Yes?

So under the UNA, an expression like

  AxEy:x=y

will be false, but ordinarily it would be true. So ... that's going to be weird.

In fact, it occurs to me that the UNA can be expressed with a rewrite rule
with an inequality and an implication. Thus:

   AxEy:x=y

with the UNA assumed is the same as

  AxEy:x!=y -> x=y

without the UNA assumed.

This makes it clear that the UNA makes first order languages less expressive.

Marshall Received on Sat Jun 14 2008 - 02:25:14 CDT

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