confused by interchangeability among rule systems

Hello,

I'm now working on a rule system, hopefully to provide support for
bi-directionally mapping with a variant which has a sub-dialect of RIF-BLD (
http://www.w3.org/2005/rules/wiki/BLD). Specifially, we mean this
sub-dialect to be obtained from RIF-BLD by removing support for (1) equality
formulas in the rule conclusions (while still allowing them in conditions);
and (2) function constant (aka functor). As well, we mean this variant to be
obtained from RIF-BLD by adding support for (1) negative atom in the rule
conditions; and (2) aggregation (like COUNT in SQL) in the rule conclusions.

Not surprisingly, such a rule system appears as Datalog, while thanks to the
two-argument directive Import of RIF-BLD, we would provide support PROFILE
of OWL DLP where OWL DLP < OWL DL cf. RIF Profiles of Imports (
http://www.w3.org/2005/rules/wiki/SWC#Profiles_of_Imports).

So far, we prefer to adopt our existing sysntax for internal rule
processing, and when exported, the RIF-BLD syntax would also be provided.
For a light-weighted version, we follow the simplest EBNF path of RIF-BLD,
and below is an example.

 RULE      ::= CLAUSE
 CLAUSE    ::= Implies
 Implies   ::= ATOMIC ':-' FORMULA

Now, my understanding is that, for RIF aims to interchangeability, we are
allowed to keep our internal rule processing with output of (valid) RIF
documents. Once external other RIF documents arise, our system needs to
normalize them for our internal rule processing. Back to our bi-directional
mapping with a variant which has a sub-dialect of RIF-BLD, as shown in the
attached here-we-are.jpg, we feel free to interchange ours, i.e., Rule
System #1, with other Rule System #2 and #3. However, for the rest, such as
Rule System #4 - #8, each has a bi-directional mapping with another variant
which has another sub-dialect of RIF-BLD, we are confused by how much we
could interchange between ours and others. Is it intersection of two RIF-BLD
sub-dialects? Note that such an intersection of two RIF-BLD sub-dialects is
not necessarily the RIF core. Even worse, for Rule System #9 - #15 in
RIF-PRD, is the interchangeability ensured by intersection of our RIF-BLD
sub-dialect and their RIF-PRD sub-dialect? If so, then I am afraid that we,
by ourselves, have to specify a lot RIF-BLD sub-dialects and RIF-PRD
sub-dialects for interchangeability among RIF-aware rule systems. Such a
solution, of course, does not take (as much as possible) advantage of RIF
existing specifications.

Most possibly, i misunderstood something, and I appreciate a lot for your
suggestions.

btw: the attached here-we-are.jpg is what i copied from "The state of the
Semantic Web" (http://www.w3.org/2008/Talks/0307-Tokyo-IH/Slides.pdf) with
my homework done at Page 54.