Stating the model theory free from lexical categories (was: Re: [SCL] Re: Observation)

[pat hayes]

>On Tue, Jun 03, 2003 at 02:50:49PM -0500, Pat Hayes wrote:
>>  Chris, after the talk to day I now see what you have been talking
>>  about and why you have been saying these odd-to-me-sounding things
>>  (and, no doubt, vice versa). ... Rather than answer your email
>>  point-by-point, let me try to give an overview of my way of talking,
>
>It is definitely just a way of talking -- a very reasonable one, I
>agree.


>Right, fine; you are just describing a lexicon "backwards".  Instead of
>starting with a predefined lexicon with its determinate lexical
>categories, you want to look at a set of axioms and extract the lexical
>catetories.  This is essentially what I was talking about with my
>awkwardly-named principle of "least type-freeness".

Right.

>  >
>>  In this way, the ontology contains its own implicit 'declarations' of
>>  the syntactic role of the terms in its vocabulary and also of whether
>>  or not its language can be understood as a TFOL language. The
>>  syntactic role of a name is not fixed by prior (invisible) fiat when
>>  defining a 'language' in your sense:
>
>Or, equally, it was as fixed before as after, we just didn't happen to
>know which language was relevant til we saw the ontology.

Well, yes; what worries me is that if we then read another 
expression, we have to be ready to say that the language 'changes', 
which makes my hair stand on end.

>
>>  So the very *idea* of a symbol having a pre-ordained syntactic
>>  'category' isn't needed in SCL (still less so in CL),
>
>It is, as you have already said, a convenient and harmless abstraction.
>
>>  and in fact it gets in the way.
>
>Not for the definition of the model theory -- though it might be the
>case that people are misled into thinking we are talking about
>implementation.
>
>>  This is the major reason why Ive always disliked your use of the
>>  textbook "language" terminology, by the way: the fact that each (S)CL
>>  ontology wears its syntax on its sleeve, as it were, is a major
>>  feature of this thing we have been building, and the 'logical language
>>  signature' way of talking obscures that feature.
>
>I don't believe anything we've done to this point contradicts that.  But
>it might be a good thing to reflect this point more strongly in our
>approach.  But I'm just not sure how it would work.  Practically
>speaking, one starts with an ontology, a set of formulas.  But a formula
>is typically something defined in terms of an antecedent lexicon.

Well, we only need to make the distinctions antecendently which are 
required in order to parse the input. The individual/relation name 
distinction isn't required since we can read it off the syntax.

>
>>  As you know, I havnt liked your 'standard' way of defining languages
>>  from day one, but Ive shut up about it because its just us guys
>>  talking and you are the one writing the documents. But I think that we
>>  have got to a point where we have to get this thrashed out, because
>>  this notion of a logical language is now causing problems. SCL isn't a
>>  language in this sense: its an ontology notation with a model theory.
>>  The 'languages' are just side-effects of ontologies.
>
>I really don't know how to write things up much differently.  Where does
>the notion of a formula come from?

I'll try to sketch it this weekend.

>
>>  >Granted, we don't stipulate overlap relations between lexical
>>  >categories in SCL, because SCL permits any kind of overlap in its
>>  >instances; but a *given* lexicon will have to stipulate those
>>  >relations explicitly -- theoretically at least.
>>
>>  I disagree, see above. In fact I don't think we even need the idea of
>>  a lexicon (other than some kind of global lexicon to enable a parser
>  > to distinguish names from eg whitespace.)
>
>Well, *that* might be true, but the point is that you DO need a lexicon
>of basic syntactic elements to bring any semblance of order to the
>language and its semantics.

We are in a slightly odd position here, though, in that we have 
'lexical' categories which are allowed to overlap. That is, we have a 
*category* which can't really be identified with a predefined set of 
strings. Maybe we need an intensional notion of a lexicon (??I can 
hardly believe that I just typed that, but that's what it seems to 
say...)

>
>>  It would be OK to have a notion of the lexicon of an interpretation,
>>  actually; but it has to be understood to be a semantic notion, not a
>>  syntactic one.  The lexical category of an interpreted symbol is
>>  defined by the interpretation mapping,
>
>I'll try to work the details of the idea out.

On reflection, this is really just the old CL idea of merging the 
lexical categories of individual and relation symbol categories, 
thought of as a pre-defined lexical categorization; but it allows us 
to 'classify' them into categories depending on how they are used in 
an expression. You know, we didn't ought to find this troublesome 
since we do exactly the same, in effect, for terms and atoms. You can 
only tell them apart by looking at their surrounding context.

In a nutshell: the syntax depends on having syntactic categories of 
relationName and individualName. BUt these are syntactic categories 
rather than lexical categories. Making them be lexical categories is 
a decision for a particular concrete syntax to make: some may, but 
this is not required by the abstract syntax. Make sense?

>  > PS. BTW, the reason we weren't communicating, I think, is that I have
>>  been consistently understanding 'relation symbol' to mean 'symbol
>>  which occurs in a relation position in some sentence', whereas you
>>  have been consistently thinking of it as meaning 'symbol which is
>>  categorized as a relation symbol in the language's lexicon'.  --
>
>That's part of the story, but doesn't explain everything.  I think a
>more accurate explanation is this difference in standpoint.
>
>I'm very tired and fuzzy-headed as I write this, so I'm not at all
>confident of its coherence...

Hey, it sounds great to me :-)

Pat
-- 
---------------------------------------------------------------------
IHMC			(850)434 8903 or (650)494 3973   home
40 South Alcaniz St.		(850)202 4416   office
Pensacola              			(850)202 4440   fax
FL 32501           			(850)291 0667    cell
phayes at ai.uwf.edu	          http://www.ihmc.us/users/phayes
s.pam at ai.uwf.edu   for spam