[SCL] Headers and bodies

[Bill Andersen]

Hi, everyone..

Man, it's tough just trying to read all the text Pat can generate much 
less understand it and reply to it, but here goes.  I have some 
comments on what (I think) I understand so far..

> First, define basic SCL as the language which has a single category of 
> names, and the MT is defined so that terms which occur in a relation 
> position must denote relations, and in object position must denote 
> something in the universe of discourse (and function symbols denote 
> functions, of course), and no other constraints. Call this 'basic SCL' 
> and 'an SCL interpretation'or just 'an interpretation' of a set of SCL 
> sentences. There are no fixed arities or any such other complexities 
> in basic SCL; those are handled by the use of headers.

Not sure about the headers yet, but I like the idea of the single 
category of names.  To anticipate some of Pat's later comments, it 
often comes up in practice that ontologist A writes an ontology where 
what would conventionally be taken to denote kinds are meant by them to 
denote individual things.  For example:

   Chemical:
     Hexokinase
     SodiumChloride
     ...

   Model:
     F-150
     Taurus
     Explorer

These "individuals", for another ontologist B, would be kinds.

> A. Every SCL document/ontology (we need a better word; I'll use 
> 'document' for now) consists of a header plus a body, written <H,B>, 
> both of which are themselves documents. The body is (a set of) SCL 
> (sentences), and the header must supply enough syntactic information 
> to enable a generic SCL parser to parse the SCL in the body.  'Parse' 
> here includes allocating relation symbols and individual symbols to 
> the appropriate category if that is required by the particular 
> language. An interpretation of an SCL document is an interpretation of 
> the body which satisfies the constraints described by the header.

This might not be so simple.  If I have:

   (forall (?r ?x ?y)
     (=> (reflexive ?r)
         (=> (?r ?x ?y) (?r ?y ?x)))

   and

   (reflexive nextTo)

In the same ontology, it's not apparent from the parse that nextTo is 
supposed to be a relation symbol without knowing something (semantic) 
about the ontology in question, namely (=> (reflexive ?r) (relation 
?r))

> B. Headers may cite one or more 'standard' headers of some kind (via a 
> URL), or they may be local to the document. If a document is split 
> into parts, each must have an appropriate header attached to it.

Good.

> Obviously this would allow arbitrarily complex conditions to be 
> labelled as 'syntactic', so we will only impose conformance on a 
> narrowly defined subset of all possible SCL headers; but the idea is 
> general-purpose.

Forgive me for perhaps not studying what Pat wrote thoroughly enough, 
but I'm not sure that what he's talking about doesn't entail arbitrary 
semantic conditions, or at least the presence of some small 
super-ontology that distinguishes between relation and individual.

[lots of good stuff skipped]

> -----
>
> We could get more ambitious, by invoking other things in the header, 
> such as
>
> concat (a function on strings)
> dequote (a function)
> with conditions:
> concat is concatenation of strings
> <I(s),s> in ext(I('dequote')) whenever I(s) is defined, otherwise 
> <s,s> in ext(I('dequote'))
>  and then we can do things like:
>
> Relation names all begin with an uppercase letter:
> Upcase(?x) iff (?x='A' or ?x='B' or ... or ?x='Z')
> Rel(?x) implies (exists (?y ?z) (Upcase(?y) and 
> ?x=dequote(concat(?y,?z)) ))

How about the case:

   Rel(Foobar)
   Rel(foobar)
   =(Foobar,foobar)

You'd need an additional axiom constraining relations to only have one 
name.

In general, I'm not sure that all of this is making things any simpler. 
  Perhaps so and I'm not understanding fully, but it seems to be 
blurring the line between language and content, or between 
meta-language and language.  I will study the rest more thoroughly and 
make comments (and/or correct my comments).

   .bill