Re: POOD and the Unique Name Assumption
Date: Wed, 11 Jun 2008 20:55:25 -0400
"Marshall" <marshall.spight_at_gmail.com> wrote in message
> On Jun 10, 5:05 pm, "Brian Selzer" <br..._at_selzer-software.com> wrote:
>> "Marshall" <marshall.spi..._at_gmail.com> wrote in message
>> > On Jun 9, 6:02 am, "Brian Selzer" <br..._at_selzer-software.com> wrote:
>> >> Does the Unique Name Assumption apply only to individuals, or does it
>> >> apply
>> >> also to relations? Under an interpretation where constant symbols are
>> >> mapped to individuals and predicate symbols are mapped to relations,
>> >> if a
>> >> and b are constant symbols and P and Q predicate symbols and if
>> >> neither
>> >> aPb
>> >> nor aQb fail to denote, can aPb ever mean exactly the same thing as
>> >> aQb?
>> >> And if the Unique Name Assumption does apply also to relations, then
>> >> what
>> >> impact does that have on POOD?
>> > 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, when combined with the Closed World and Domain Closure assumptions provides the basis for answering negative queries and queries that involve counts. For example, if you issue a query like
"How many widgets are blue?"
against a relation containing widget names and colors, but widget names do not follow the unique name assumption, then more than one widget name could reference the same widget, and thus even though the names are unique, the number of widgets could be completely different than the number of widget names. Consequently, you can't rely on the answer without the Unique Name Assumption. A query like,
"How many widgets are not blue?"
can be answered only when all three assumptions are in effect. The Domain Closure Assumption and Closed World Assumptions make it possible to determine which widget names denote and which widget names that denote are associated with a color that is not blue, but it is only under the Unique Name Assumption that the actual count of widgets that are not blue can be calculated.
>> > But ordinarily, the mapping from names to things being named
>> > is a function, but not necessarily the reverse.
>> > As to whether aPb can ever mean the same thing as aQb:
>> > 2+0 = 2-0
>> The /result/ of 2+0 is the same as the /result/ of 2-0, but is the
>> of an expression the same as the result of the expression? It seems to
>> that how one arrives at a result can be just as important as the result.
>> For example, if a man turns left onto the sidewalk in front of his house
>> then proceeds around the block, he will end up at the exact same place as
>> he had turned right onto the sidewalk and then proceeded around the
> "2+0" != "2-0"
> 2+0 = 2-0
> It seems straightforward enough. "2+0" and "2-0" are two
> different names, expressions specifically, for the same thing.
Received on Wed Jun 11 2008 - 19:55:25 CDT