Re: an answer to the datatype question, plus a rationale

Peter F. Patel-Schneider wrote:

>
> I believe that the most important thing to get right is the *treatment* of
> literals.  This may result in different answers to A and D, and even
> different potentially different kinds of answers to A and D.  I am
> providing the answer below partly to show that a different reading of
> literals can change the answer to the question.

It first reading, this seems an entirely appropriate way to look at the
issue.

>
>
> ANSWER:
>
> Under a treament of literals that has a literal denote a set, namely
> (potentially a superset of) the set of data values that some datatype maps
> the literal to, the answer to A is YES.  The technical answer to D is NO,
> but the real answer to D is YES, in that the denotation of _:a is a
> (probably a singleton) subset of the denotation of "10", and thus _:a and
> "10" are `the same,' under a reasonable reading for `the same.'
>

Yes.

Attempts for "untidy" literals seem to arise from the desire:

numberOfViewings(x)  not-equals titleOf(x) where _x_ is a movie whose title
is "10"

but as Drew McDermott correctly points, out, there is no _syntactic_
distinction between

"10" the integer and
"10" the string

so while the token "10" can map to both an integer and a string, the
value-set is the same for the value of both functions, hence these _must be_
equal.

I strongly agree that your general framework for analyzing the problem is
the one that needs to hold sway.

Jonathan