[SCL] Proposed additions to the SCL draft standard

[pat hayes]

>Folks,
>
>Tanel's suggested additions to the SCL draft standard are also
>on the list of features that are needed to support conceptual
>graphs.  It's fine to have a minimalistic "core" semantics,
>but the standard should also include some commonly used
>extensions to the core.  If they're not included in the
>standard, every language that needs them will have to
>implement them independently (and probably incompatibly).

I believe we had already broadly agreed to have all three features 
you outline. I have some quibbles with details.

>
>Some comments relevant to CGs:
>
>  1. Integers are essential for the overwhelming majority of
>     practical applications, and some means of accommodating
>     them must be provided.  There is, however, a question of
>     whether the standard should support full integer arithmetic
>     as defined by Peano's axioms or whether it should allow
>     for some limited subset.

The applications I am aware of do not require anything like the 
sophistication  of a full arithmetic. I think it will be sufficient 
to provide numerals/integers as a built-in datatype perhaps with one 
or two associated functions such as addition and the less-than 
ordering; but the associated procedures are only required to work on 
actual numerals in the lexical space of the datatype, note: they are 
not required to be able to solve Diophantine equations of arbitrary 
complexity. That will be quite sufficient for things like numerical 
quantifiers and DL-style cardinality reasoning.

>     I believe that full arithmetic must be available, along
>     the lines of the Z standard

I disagree. We can of course allow people to refer to a standard 
arithmetic ontology, and even to provide one, but it should not be 
built into the model theory or the syntactic conditions (in contrast 
to a datatype, which will be.) That would place much to high an entry 
barrier for implementers.

>, which includes a library of
>     theories for integers, sets, and sequences.  I recommend
>     adopting at least the Z library as an option, but we might
>     also have a more limited subset in the core that would be
>     sufficient to define quantifiers such as "exactly N" or
>     "at least N but no more than M".  People have been using
>     such notations in CG extensions for a long time, but we
>     have to standardize them.

We have to standardize the notations and their intended meaning. To 
do that we do not need to have a particular ontology standardized, 
however.

>
>  2. Comments (including "structured annotations") are essential
>     for most practical applications.  We have defined a version
>     of comments for CGs, but there are still some issues about
>     how fine-grained the commenting should be -- i.e., whether
>     comments at the level of complete formulas are sufficient
>     or whether comments can be attached to smaller syntactic
>     units.  In CGs, for example, the box and circle notation
>     makes it convenient to add comments to smaller units.
>
>     But it would be best if some level of comments could be
>     associated with categories in the abstract syntax so that
>     they could be preserved in cross-language translations.

I agree. We already have a proposal to allow such commenting.

>
>  3. The free-form SCL syntax, which allows quantifiers to
>     range over any kind of entities (individuals or predicates
>     indiscriminately), allows assertions that are unusual and
>     certainly unexpected for people who use other versions of
>     logic (including both conceptual graphs and traditional
>     predicate calculus).
>
>     To accommodate traditional predicate calculus as well as
>     languages with various type conventions (including CGs and Z)
>     the standard should include the definition of restricted
>     quantification as an option.

I agree, and we had already decided on this. The recent version of 
the abstract syntax have been deliberately formulated with this 
requirement in mind.

>  I don't believe that we have
>     to support the strict typing of Z,

I agree; that would be inappropriate for us.

Pat


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