[SCL] Re: two comments

[Chris Menzel]

On Tue, Nov 04, 2003 at 02:03:31PM -0600, Pat Hayes wrote:

I like all this stuff:

> 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. For 
> example, a local lexicalization might write variables using a prefix 
> ?, relation names using initial uppercase, individuals using initial 
> lowercase and no punctuation, and function symbols using the prefix 
> 'fun-', so that elements of each lexical category can be recognized 
> in isolation, permitting easy parsing.  But a non-local 
> lexicalization might not make any distinction between the lexical 
> forms for individuals, functions and relation names, and rely 
> entirely on the SCL grammatical context to assign these roles. In 
> such a language, the Horrocks sentences are self-correcting, in a 
> sense: if one writes
> 
> (x y) x=y & P(x) & not Q(x)
> 
> then x and y must be individual names, 

"variables", of course.

> and P and Q must be relation names, but whether or not they are
> individual names is open. They might be, but there are no satisfying
> interpretations in which they are. But they also might not be, and so
> this is satisfiable by an interpretation which makes P and Q into
> relation names but not individual names.  But if we add
> 
> (x y) x=y & P(x) & not Q(y) & R(P,Q)
> 
> then it is no longer satisfiable, since this sentence only admits 
> interpretations in which P and Q are classed as individual constants 
> as well as relation names. But note, this is the *same* language, in 
> this account: the language does not change when the extra conjunct is 
> added, it just has fewer satisfying interpretations (as one would 
> expect, of course).  P and Q are still in the category 'predicate 
> constant'  as they were before, but they are now also required to be 
> in the category 'individual constant'.

I think I grok your point, but I'm not sure that the definition of
"language" have been pinned down tightly enough to give the thesis here
a definite truth value.  So: what, exactly, is a language?  Answer must
entail that the two sentences above are sentences of the *same*
language.

> Chris, I know this is unconventional, 

But it's cool, and will be very handy if we can make it work.  I've got
no particular fondness for convention beyond the fact that it is
familiar and hence easy to start with.

> but I think it is important to allow this flexible case without
> breaking the underlying SCL model 

Strongly agree.

> For us, a language *is* anything that can  be made to fit our AS
> structure. 

Ok, that's the start of an answer to my question above. :-)

Will study the rest of your post over the next few days.  Teaching is
very time consuming right now, unfortunately.  And you guys are making
my brain hurt with these rapid fire exchanges!

-chris