[SCL] Re: two comments

[pat hayes]

>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.

whoops, right.

>
>>  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?

Good question. I'll try. Roughly, an expression of a (concrete) 
language is anything that can be parsed into the AS categories using 
the parser which defines the syntax of the language.  Anything: so if 
your parser can parse rocks, then the expressions of the language are 
the rocks it can parse.

So the honest answer is: I don't know what 'a language' is. It can be 
any set of things. I do know what counts as an SCL-kosher parsing, 
however: its some assignment of 'pieces' of the 'things' to the SCL 
AS categories, ie a way of reading the things as fitting into the 
syntactic categories.  So in the above example, the expressions 
(things) are character sequences, and the parsing can be done by some 
BNF. Now, there is a slight nasty, in that on this picture, with the 
categories we currently have, the first example above is 
syntactically ambiguous. It has one parsing in which P and Q are in 
the category predicate-constant and not in individual-constant, and 
it has a different one in which they are in both categories. Since 
these are grammatical categories, this is a genuine syntactic 
ambiguity. So if we have to have a context-free language then this 
can't be done with this grammar.

We could get over this by being having just a single category of 
'constant', and let the interpretations distinguish between the 
cases, which is what I had in mind when writing the previous message. 
This would be in line with the basic 'extendable lexicon' intuition. 
This however would be a step back to the CL wild-west syntax, which I 
guess we should try to avoid (?).  Or we could just accept it, and 
remark that unambiguous context-free parsing requires that the basic 
categories can be assigned unambiguously in a context-free way (duh), 
and hence *derive* a conventional FO syntax from this syntactic 
condition.

I'll think about this for one more day then I will either make a 
genuine proposal or else give up.

>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.

OK then I will try harder.  :-)

>
>>  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!

Well, join the club. My brain has been hurting for years.

Pat

>-chris


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