AW: Outcomes from 12/19 telecon

Hi Chris and Hassan,

In the spirit of regarding slots as (named-argument) syntax (cf. charter)
and of keeping things simple in Phase 1, I think that slotted arguments
should for now reflect the ‘closed’ semantics of positional arguments.

This is further explained below through inlined ‘HB>’ comments.

Using ‘closed-slot’ semantics, if n is the maximum arity in a positional
system, we can round-trip
s(t_1, …, t_i, …, t_n)
(via the pos2slot shortcut) to
s{1->t_1, …, i->t_i, …, n->t_n}
and (via the slot2pos transformation), since 1<…<i<…<n, back to
s(t_1, …, t_i, …, t_n).
If n is less than the maximum arity, we end up in a ‘replenished’
normal form (with ‘_|_’ elements for the missing higher positions),
s(t_1, …, t_i, …, t_n, _|_, …, _|_).

Best,
Harold


-----Ursprüngliche Nachricht-----
Von: public-rif-wg-request@w3.org im Auftrag von Hassan Aït-Kaci
Gesendet: Di 19.12.2006 22:16
An: Chris Welty
Cc: Public-Rif-Wg (E-mail)
Betreff: Re: Outcomes from 12/19 telecon
 

Chris Welty wrote:

> The telecon discussion went on quite long today and we didn't have time 
> for everything on the agenda.  I felt like we were near resolution on a 
> few issues but didn't quite get there, so I'd like to summarize where I 
> think we are. Overall I'm quite happy to see that we are finally 
> starting to deal with concrete technical issues.

Hi Chris,

I agree and share the feeling. I also agree that reviewing where we now
stand excatly is in order.

> Hassan proposed at the f2f to use constraints as a way to connect a 
> keyword syntax with a positional syntax, by mapping positional syntax 
> into keyword syntax. 

HB> In the F2F4 breakout session we considered the positional-to-slotted
HB> mapping (pos2slot), assuming i<n, from
HB> s(t_1, …, t_i, …, t_n) to
HB> s{1->t_1, …, i->t_i, …, n->t_n}.
HB> Here, the curly braces {…} express both:
HB> * An unordered collection of the slots i->t_i
HB> * An application of s to the slots i->t_i
HB> Each natural-number slot name i stands for rif:i, but can also be
HB> regarded as rdf:_i, argi, or as a similar positional name.

> Harold later found that the specific syntax 

Not "syntax" but "semantics" of \psi-terms (which are equivalent to OSF
constraints in solved form). The \psi-term syntax is a simple generalization
of the FOT syntax:

	Psi ::= X:s(f_1=>Psi_i, ..., f_n=>Psi_n)

(one may use '=' instead of :, and -> instead of => - matter of taste)
where X is optional and n can be 0. Like FOT, these constructs can be
used to model data with all kinds of intended semantics, and well-formedness
conditions may be added (like fixed/flexible arity, partial/total features,
etc, ...) in the same way a *schema* or DTD describes well-formed elements.
Such well-formedness can be enforced using (static or dynamic) constraint
normalization rules. Hence, a rather expressive family of different semantics
can thus be ascribed to the above "slotted" syntax depending of the signature
axioms making up the desired schema. My point thus is that this is a cleaner
and simpler solution to accommodate various differring behaviors for the
same syntax. In particular, there is no need for contrived notational tricks
such as proposed by Harold (some kind of continuation variable notation).
Notwithstanding whether it is correct and/or would work as he intends, it
is a hack to accommodate just one specific semantic discrepancy (viz.,
flexible or open arity vs, fixed arity symbols). What about other possible
discrepancies? Shall we introduce a hack to accommodate each one that we
recognize? I don't think so! By contrast, using well-delineated schema
constraints for enforcing well-formedness and other such integrity
constraints is both more expressive (simply specify the signature
constraints for your desired semantics), and simpler. Finally, since
the above slotted syntax is simple and can be mapped to several differring
semantics of slotted terms depending on its symbol signature schemata,
I thought it would be a good candidate for the minimal slotted syntax
we are after. How this minimal syntax is desugared in the (normative)
constraint form depends on the semantics enforced by the chosen signature
schema, and its solving semantics on that of the constraint system it
desugars into.

Therefore, Harold mistakenly understood that I was proposing a semantics
for slotted terms.

> proposed by Hassan created a problem with unifying variable arity 
> predicates, that is that (P x y) would unify with (P x),

HB> For an ‘open-slot’ (or ‘subsumption’) semantics of slotted forms
HB> s{1->t_1, …, i->t_i, …, n->t_n} unifies with s{1->t_1, …, i->t_i}.
HB> Assuming that the above pos2slot mapping is employed to interpret
HB> positional forms as a shortcut of (position-named) slotted forms,
HB> s(t_1, …, t_i, …, t_n) would wrongly unify with s(t_1, …, t_i).
HB> For a ‘closed-slot’ semantics this problem does not arise, since
HB> the above slotted forms would no longer unify, so their shortcut
HB> versions wouldn’t either.

> and Harold 
> proposed a solution that maps keyword syntax into positional.  A few of 
> us were unsure on the telecon today that the proposal as it stood (using 
> 'bottom' to substitute for missing parameters) would work, as bottom 
> unifies with nothing, which would create unexpected results compared to 
> keyword systems.

HB> This slotted-to-positional mapping (slot2pos) can be employed, for
HB> a ‘closed-slot’ semantics of slotted forms, to avoid that slots need
HB> to be dealt with in the model theory.
HB> Currently, ‘_|_’ or owl:NOTHING is used as a distinguished element
HB> for slots missing in (positionalized) forms to express their ‘N/A’-like
HB> NULL-value interpretation: ‘_|_’ is equal to itself, and unequal to any
HB> ordinary (non-‘_|_’) term.

> Hassan suggested that keeping the mapping of positional 
> onto keyword would work if we also introduced function signatures, which 
> could prevent unifying a binary predicate with a unary one when it 
> mattered.  Harold has not weighed in on that counter proposal yet.

HB> Indeed, using the Prolog-like notation s/a for an s of arity a,
HB> s/n{1->t_1, …, i->t_i, …, n->t_n} doesn’t unify s/i{1->t_1, …, i->t_i}
HB> and with this ‘locally-closed-slot’ semantics imposed by s/n and s/i
HB> s/n(t_1, …, t_i, …, t_n) would no longer unify s/i(t_1, …, t_i).

I hope the above explanation will help.

> Michael expressed some concern that the CLP formulation would not handle 
> model theories for WFS. (was that right?)  Hassan was unsure and will 
> try to find the answer.

I have to communicate off line with Michael about that.

> We discussed for a while the idea of treating constraints as an 
> "external call".  This seemed to concern several of us, but I think the 
> confusion was cleared up as just overloading of "external call" - here 
> the idea is that constraints as part of RIF rules allows RIF to treat 
> data models and languages as orthogonal.

Yes. This is the essence of it.

Thanks for your summary.

-hak
-- 
Hassan Aït-Kaci
ILOG, Inc. - Product Division R&D
tel/fax: +1 (604) 930-5603 - email: hak @ ilog . com