[SCL] Approach to a concrete syntax

[Chris Menzel]

On Wed, May 21, 2003 at 06:09:55PM -0500, Pat Hayes wrote:
> ...
> >Okay, I'm fine with that. The only alteration to the syntax that Chris
> >has proposed that I'd make would be to generalize the quantifiers,
> >connectives, and predicates to take a typing parameter
> 
> Can you say why? That seems a slightly crazy idea to me, I have to 
> confess. That set - quantifiers, connectives and relations - doesn't 
> seem like the kind of class I would be tempted to generalize over. It 
> reads like 'sheep, fish and pieces of copper', you know?

I had understand Murray here to be referring to generalizations for each
of these categories.  In the current DTD, I have "forall" and "exists"
as distinct elements; similarly for the boolean connectives.  I think
Murray is suggesting a more general element for *each* these categories
with attributes whose values are the corresponding logical operators;
something like this:

<!ELEMENT formula (boolean | quantifier | atom)>

<!ELEMENT boolean (formula*)>
<!ATTLIST boolean type (and | or | implies | iff | not) #REQUIRED>

<!ELEMENT quantifier (varlist, formula)>
<!ATTLIST quantifier type (forall | exists) #REQUIRED>

A small problem here is that current SCL spec requires exactly two
arguments for conditionals and biconditionals, and exactly one for
negations, but of course we could adopt simple and obvious conventions
for interpreting all three with arbitrarily many arguments.

I don't have any idea what Murray has in mind by a generalization of the
predicates, as they all already fall under the single element <predcon />.

-chris