[SCL] two comments

[Tanel Tammet]

Hi,

pat hayes wrote:
> Rather than drafting yet another version, let me put on record some of 
> the changes Id like to see.  I'd be happy to attempt a rewrite when the 
> text settles down.
> 
> First, as currently phrased the AS describes a lexicon as a collection 
> of sets. I would prefer that we treat the AS as a purely abstract 
> algebraic structure, in which the 'basic' items are considered to be 
> grammatical categories - categories of expressions - rather than sets of 
> syntactic entities. The makes no difference to the formal stuff but 
> simplifies the AS and makes it more uniform, and avoids what is 
> otherwise a potentially awkward set of issues concerning the 'status' of 
> lexical items in some concrete SCL languages.
> 
> A concrete SCL language is then obtained by providing a 'lexicalization' 
> which provides for a set of wf expressions and a way to parse any such 
> expression into an SCL AS structure.  Now we can distinguish two kinds 
> of lexicalization: those in which the primitive syntactic elements (the 
> things in the 'lexicon') can be recognized in isolation, and the others. 
> Call the first 'local' for now. 

This was really a message to Chris, but I cannot help
intervening :-)

When you speak about the "purely abstract algebraic structure"
etc then I honestly do not understand what do you exactly mean.
I won't understand it until I see the AS presented in this form.

Now, when we get to see AS in this form, and it uses anything
uncommon, people will have hard time reading it. Before I see
AS in this particular suggested form, I guess that it is safer
to stick with what prospective readers are used to. In the
context of a spec aimed to be used as a standard, being as
widely understood as we realistically can is IMHO more important
than being clever.

> Chris, I know this is unconventional, but I think it is important to 

Again: being unconventional is bad.

> has the nice feature that when you use it everything gets simpler and 
> nagging problems just go away, with no real cost, which is always the 
> sign of having got something right :-).  Just forget the doctrine that a 
> language *is* a set of strings. 

We could forget that, but readers probably won't.

> The same effect could be achieved by axioms of the form
> holdsn(x y1 ... yn) implies ind(yi)
> i.e. by embedding SCL into a FO theory rather than into SFOL itself, 
> with a suitable modification to the statement of correspondence between 
> full SCL and the holds/app translation.

Do you really want to distinguish ind, fun and pred constants?
I cannot see how such a distinction will make things simpler
for SCL. It is simpler to have fewer different categories,
not more.

If you really want to distinguish them, then we could
always use SFOL, where they are nicely distinguished.

> However, contra Tanel, it seems to me that this is not really an issue 
> requiring any changes to equality: rather, it is to do with the range of 
> quantification. What it boils down to is that in the holds/app 
> embedding, all quantifiers should be understood as restricted to a class 
> which is not obliged to contain entities which occur only in the first 
> argument position of any holds or app assertion. 

You are most probably right that this restriction on
quantification may work (we talked about it briefly on way from Tampa).

Bur I am still having an opinion that it is easier to have
two equalities and "ordinary" quantification than one
equality and "unordinary" quantification. Quantification
is more important than equality, ergo we should prefer
to keep quantification as simple as possible, not
equality.

Regards,
          Tanel