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report on coverage issue

From: Ginsberg, Allen <AGINSBERG@imc.mitre.org>
Date: Mon, 18 Sep 2006 12:36:41 -0400
Message-ID: <90A462F2D6E869478007CD2F65DE877CF94E71@IMCSRV5.MITRE.ORG>
To: <public-rif-wg@w3.org>

Hello All,

In regard to the action:

[NEW] ACTION: aginsber to gather definitions of covers and propose a
synthesis [recorded in
http://www.w3.org/2006/09/12-rif-minutes.html#action11]

Please review the following report. Thanks, Allen.



Report on "Covers" Issue

1. Original statement of the issue

According to
http://www.w3.org/2005/rules/wg/wiki/Design_Constraints/Terminology :

"A ruleset is covered by a RIF Dialect if that dialect can be used to
faithfully convey that ruleset. (Exactly what it means to "faithfully
convey" the ruleset still needs to be refined.) A language is covered
by a RIF Dialect if and only if all rulesets which can be written in
that language are covered."

So here the issue is left in terms of coming up with a definition of
"faithfully convey."


2. Subsequent proposal at F2F3

Here are the contents of a slide by Christian:

< RIF covers L > means that any expression E1 in L can be mapped into a
RIF fragment and back into an expression E2 in L that is equivalent to
E1 according to the semantics of L (and thus, may be identical)

< RIF covers L1 and L2 > means that, if there is a mapping from L1 to
L2 that is semantic preserving in some sense, any expression E1 in L1
can be mapped into a RIF fragment and back into an expression E2 in L2
that is equivalent to E1 in the same sense

 

3. Discussion of Christian's proposal

i) It seems to me that these "definitions" should actually be derivable
from a more fundamental defintion of the notion of coverage. 

ii) The defintions should be stated using the notion of WFFs
(well-formed formulas) instead of "expressions" and "fragment."


4. Alternative approach (Model-based approach)

Let R be a set of WFFs in some language L. Let M be the set of all
models of R (according to the semantics of L).

Let R' be a set of WFFs in the RIF (or some dialect thereof). Let M' be
the set of all models of R' (according to the semantics of the RIF or
the relevant dialect thereof). 

Then R' "faithfully conveys" R if and only if M = M'. The RIF "covers"
L iff for every set of WFFs in L there is a set of WFFs in the RIF that
faithfully conveys the former.


5. Discussion of Model-based approach

i) It is probably too restrictive. It is probably enough for the two
sets of models to be isomorphic. But this is a relatively minor point.

ii) It is an "ontological" statement, i.e., it says "what it is" for
two sets of WFFs to be related in a certain way. How, in practice, one
would prove that the definition holds in a particular case is another
matter. 

iii) Also, even if we know that a language L is covered by the RIF in
the model-theory sense, it doesn't follow that there is an algorithm
for translating from L to the RIF (and back). That seems to me to be
yet another issue. 


6. Synthesis

There is a difference between saying that the RIF covers a language L
in the sense of "faithfully convey," and saying that rulesets in L can
be translated into the RIF (and vice versa) algorithmically. Whatever
definition of "coverage" (or alternative terminology) we ultimately
choose, we need to show that we are aware of this distinction. Perhaps
"Coverage" as a goal should be broken into two goals: 1) expressivity
(corresponding to model-based notion of coverage) and 2)
translatability (corresponding to the operational notion of being able
to translate between languages).
Received on Monday, 18 September 2006 16:38:41 GMT

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