[SCL] Suggestion for SCL extension module

Tue Nov 4 05:08:16 CST 2003

Tanel Tammet wrote:
> Chris,
> 
> Hopefully we can get your version very soon now:
> we'll have some work to do on full SCL modules
> and SCL concrete syntaxes, which cannot be really
> started before.
> 
> Meanwhile I have a proposal about a full SCL
> module, which we could include. We have spoken
> about it before, but IMHO too little.
> 
> I'll give the proposal in the short and informal
> manner here.
> 
> The goal of the module would be to allow SCL
> to be extended with operators which are NOT
> defined in SCL and have no meaning for SCL.
> 
> Examples could be modal operators, negation-as-failure,
> default rules, etc etc. All of these have their
> own semantics and we cannot describe this
> semantics in SCL spec.
> 
> However, we could provide a clear slot
> to put these operators into SCL.
> 
> Why would that be good? Because:
> 
> - they are crucial for various specific applications
> - the specific logical languages using them tend to
>    contain FOL
> - hence the designers of these specific languages
>   could take adavante of SCL spec as a component
>   of their own language spec
> - systems not understanding anything out of SCL
>   could still understand PARTS of the extended
>   language.
> 
> Let me bring an example.
> 
> Suppose we have a file containing two assertions
> in a nonmonotonic logic, one of them a simple default
> rule:
> 
> ==============
> ostrich(dave).
> forall X. default-implies(bird(X),flies(X)).
> =============
> 
> Now, the first of these has perfectly clear
> semantics in FOL, while the second one does
> not.
> 
> Hence, an SCL-understanding system could
> perhaps understand this file by keeping
> only these TOP-LEVEL parts which it can
> understand (first sentence) and throw away the
> not-understood ones (second).
> 
> What would it mean semantically:
> 
> The top-level sentence containing unknown
> operators cannot be given a concrete
> truth value in the SCL-based system,
> since this would probably misinterpret
> the sentence.
> 
> However, FOL (and prop logic) can represent
> an unknown logical truth value simply as
> a propositional variable not occurring anywhere
> else, ie a new propositional variable.
> "New" here means the same as a "new" function
> symbol for Skolemization: when we give a sentence
> forall X. exists Y. P(X,Y).
> then, as we know, we can Skolemize it into
> forall X. P(X,f(Y)).
> where "f" is a new function symbol not
> occurring anywhere in the full formula
> which is interpreted.
> 
> Skolemization does not change satisfiability,
> as we know, although it brings in the
> new symbol.
> 
> The example we had before could hence be
> "pseudo-skolemized" to
> 
> =============
> ostrich(dave).
> p1.
> ============
> 
> where "p1" is a new propositional variable
> not occurring anywhere else.
> 
> After this "pseudo-skolemization" an SCL
> understanding system could still infer
> "ostrich(dave)"
> from the file above, which is a correct
> inference also in the context of default
> logic (or ANY interpretation of
> "default-implies" in any sensible
> extended logical system).
> 
> In order to allow this we should:
> 
> a) give a syntactic slot for such
>    operations, for example, by adding
>    an operator "extended_i" to the language,
>    where any "extended_i" tuple would be
>    analogous to the "formula_i" tuple.
> 
> ==============
> ostrich(dave).
> forall X. extended_3(default-implies,bird(X),flies(X)).
> =============
> 
> b) give semantics for "extended_i" tuples.
>    This is certainly harder than giving a
>    syntactic slot.
> 
>    One way to do that would be to define
>    that any tuple "extended_n(f1,...,fn)"
>    would will have  a new propositional variable
>    as a value (ie the pseudo-skolemization described above).
> 
>    Then the example would be interpreted as
> 
> ==============
> ostrich(dave).
> forall X. p1.
> =============
> 
>    where "p1" is this new prop variable
>    (we could also have "forall X. Atom_1(p)."
>    where "p" is a new constant, essentially
>    a predicate).
> 
>    Another (probably worse) way to do that
>    would be to  take advantage of the "sequence" construction
>    (file top level constructions) and define
>    that any element of the sequence containing
>    an operator "extended" anywhere will have
>    a new propositional variable as a value.
> 
>    Then the example would be interpreted as
> 
> ==============
> ostrich(dave).
> p1.
> =============
> 
> Finally, perhaps the same goals could be achieved
> using the annotations module in the SCL.
> Remember: "formula_3(annot,something,f1)"
> is equivalent to "f1"
> and "term_3(annot,something,t1)"
> is equal to "t1".
> 
> I have not really thought yet whether
> the annotation module would be enough
> or not.
> 
> Any thoughts on this theme?

Tanel,

You don't mention a way to canonically identify new language components.
The way this is done in RDF and OWL, XTM and I would hope SCL/CL/XCL is
through some unique name in a fixed namespace. The safest road from what
I can see is to use the same mechanism as everyone else has, the URI.

So, the domain of the URIs developed as part of the SCL effort plus any
extensions or concrete syntaxes developed by us would use a fixed URI
domain, and extensions or concrete syntaxes developed by others would
use a domain they control. It would be prohibited for anyone to use our
domain to develop language components. These URIs don't necessarily have
to show up in the concrete syntax itself (and of course wouldn't fit or
be appropriate in many or most cases), but should be identified in the
prose.

    http://cl.tamu.edu/docs/scl/1.0/#formula
    http://www.w3.org/2002/07/owl#Thing
    http://purl.org/ceryle/#isAuthorOf
    http://ttu.ee/scl/#ostrich

etc.  This would guarantee that two people or systems using one of the
above URIs would be talking about the same concept.

Is this close to what you had planned?

Murray

...........................................................................
Murray Altheim                         http://kmi.open.ac.uk/people/murray/
Knowledge Media Institute
The Open University, Milton Keynes, Bucks, MK7 6AA, UK                    .

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