[SWC] comments/review SWC - part2

This part 2 of the review from
http://lists.w3.org/Archives/Public/public-rif-wg/2008Jun/0126.html
covers Section 4 which wasn't covered in the first review.
More comments on the RIF-OWL embeddings in the Appendix to follow.

Axel

-- 
Dr. Axel Polleres, Digital Enterprise Research Institute (DERI)
email: axel.polleres@deri.org  url: http://www.polleres.net/

Everything is possible:
rdfs:subClassOf rdfs:subPropertyOf rdfs:Resource.
rdfs:subClassOf rdfs:subPropertyOf rdfs:subPropertyOf.
rdf:type rdfs:subPropertyOf rdfs:subClassOf.
rdfs:subClassOf rdf:type owl:SymmetricProperty.

This part 2 of the review from
http://lists.w3.org/Archives/Public/public-rif-wg/2008Jun/0126.html
covers Section 4 which wasn't covered in the first review. 
More comments on the RIF-OWL embeddings in the Appendix to follow.

Section 4
=======

*) 
"OWL (OWL-Reference) specifies three increasingly expressive species, namely Lite, DL, and Full."

Side remark, probably no rewording necessary, but doesn't OWL Lite have exactly the same 
expressive power as OWL DL? Thus, "increasingly *expressive*" is maybe not ideal wording, 
but I don't have a better suggestion.

*) 
"In the DL species, classes and properties are directly interpreted as subsets of and binary relations over the domain. "

would add a ", respectively."

*)
"The latter is a key property of Description Logic semantics that enables the use of Description Logic 
reasoning techniques for processing OWL DL descriptions."

What exactly does "The latter" refer to? better:

"This treatment is in line with Description Logic semantics and enables the use of Description Logic 
reasoning techniques for processing OWL DL descriptions."

*) 
"would change the semantics of OWL statements, even if the RIF document is empty."
->
"would change the semantics of OWL statements, even if the RIF document was empty."

*) "the interpretation of frame formulas s[p -> o] in the RIF-OWL DL combinations is slightly 
different from their interpretation in RIF BLD and syntactical restrictions are imposed on the 
use of variables, function terms, and frame formulas."

That honestly worries me. Is it wise to do that? What are the implications? Is this still FLD compatible? 
That means that RIF-OWL is not compatible with BLD? If so, in what sense uncompatible?
See also my comments below.

*)
"and that there might be particular problems in using section 3.2.2.3,"

...of which document?

Section 4.1
=======

* ) "DL-Document" 
is not so nice... I'd prefer   "RIF-BLD-DL-Document" or "RIF-BLD<sub>DL</sub>-Document"

Section 4.1.1
=========


*) "if it occurs in an atomic formula in if that is not of the form s[P -> o] or s[rdf:type -> A], where P or A, respectively, occurs in one of the ontologies in O."
->
"if it occurs in an atomic formula in the if-part that is not of the form s[P -> o] or s[rdf:type -> A] such that P or A, respectively, occur in one of the ontologies in O."

*)
"and every variable in if that is not DL-safe occurs only in atomic formulas in if that are of the form s[P -> o] or s[rdf:type -> A], where P or A, respectively, occurs in one of the ontologies in O. "
->
"and every variable in the  if-part that is not DL-safe occurs only in atomic formulas that are of the form s[P -> o] or s[rdf:type -> A] such that P or A, respectively, occur in one of the ontologies in O. 

BTW: Isn't this second part redundant? I mean, every variable in the if part for which this condidtion does NOT hold, is per definition DL-safe anyway, or no? So..?

*) I wonder if equating something with rdf:type  in a fact e.g.

   ex:a = rdf:type .
  (this is perfectly DL-safe as a fact, isn't it?)

messes up the whole "safety" section? 
Because now I could add a rule:

 ?X[ex:a eX:C] :- ?X[ex:a eX:D]

that would hurt safety, but not syntactically, or no?
What I mean to say: Isn't there an interplay with that definition 
of safety and equality in the rules language? If so, that puts the talking about safety even more at risk, 
or we need to additionally forbid nasty equalities in the rules part, at least.

Section 4.2.2
=========

*) "common-rif-dl-interpretations"

Shouldn't it be "common-rif-owl-dl-interpretations"?

*) When defining multi-structures, you use superscripts for indexes... which is kinda awkward
{I<sup>1</sup>, ..., I<sup>n</sup>}
since superscripts with numbers suggest something like "to the power"
maybe better to use subscripts after all and then separate indeces by comma,e.g.
instead of
"I<sup>1</sup><sub>C</sub>, ..., I<sup>n</sup><sub>C</sub>"
better write
"I<sub>1,C</sub>, ..., I<sub>n,C</sub>"

*) Where is "SetOfFiniteFrame'Bags" defined?!? What is the difference to "SetOfFiniteBags" from BLD and FLD, if 
your semantics doesn't specialize FLD even, it seems a bit weird to me. Not sure whether I understand what's happening here.

Section 4.2.2.2
==========

*) "As defined in (OWL-Semantics), an abstract OWL interpretation with respect to a datatype map D, with vocabulary V is a tuple I=< R, EC, ER, L, S, LV >, where"

the link to "abstract OWL interpretation" points to the rdf semantics document!!! That is probably an error.

*) "R is a non-empty set of resources (the domain); O is a non-empty subset of R, disjoint from LV"

O comes out of nowhere here, it is not a part of  I=< R, EC, ER, L, S, LV >
should it be: "I=< R, O, EC, ER, L, S, LV >"   instead???

Definition common-rif-dl-interpretation:
==========================

*) Condition 2. :  "I_truth(I_frame'(I_C(rdf:type))(k,I_C(<c>))) = t "

Note here that: (k,I_C(<c>))
is not a "SetOfFiniteFrame'Bags", at least it doesn't seem to be, since "SetOfFiniteFrame'Bags" is not defined, so I have a hard time grasping what you want to say. I suppose though, you want 

(k,I_C(<c>)) to be a shortcut for all finite bags containing (k,I_C(<c>)) in arbitrary arity >0 ?

*) Condition 3.: see above, similatry, I have difficulties with the used notation.

*) "Recall that in an abstract OWL interpretation I the sets O, which is used for interpreting individuals, and LV, which is used for interpreting literals (data values), are disjoint"

That sentence doesn't read optimal... maybe better:

"Recall that in an abstract OWL interpretation I=< R, O, EC, ER, L, S, LV > the sets O and LV, which are used for interpreting individuals and literals (data values), resepctively, are disjoint."


*) The very last example in section 4.2.2.2:
"However, the mapping EC in any abstract OWL interpretation requires every member of ex:A to be an element of O, and concrete data values may not be members of O. "

maybe better:

"However, the mapping EC in any abstract OWL interpretation requires every member of ex:A to be an element of O, and the non-empty set ot concrete data values for Data types in OWL is disjoint from O."

not sure whether this reformulation really works, but the problem with yours is that "may not be members" sounds to me like... well that doesn't imply that there is no interpretation, but only that there may be interpretations which don't work. This should be made stronger/clearer.

*) "It is currently expected that OWL 2 will not define a semantics for annotation and ontology properties; therefore, the below definition cannot be extended to the case of OWL 2. "

You countered one of my earlier questions about OWL2 with the argument that this document doesn't talk about OWL2... fine, so why you then keep still several links to OWL2 here? (Also when you talk about punning earlier), and you also don't mention OWL2 in the references. I suggest to mark all speculative references to OWL2 as editor's notes/at risk/

*) 
"Definition. Given a conforming datatype map D, a common-rif-dl-interpretation (I, I) is a common-DL-annotation-interpretation if the following condition holds

  6. ER(p) = set of all pairs (k, l) in O × O such that Itruth(Iframe'(IC(<p>))( k, l) ) = t (true), for every IRI p in V.   "

Isn't this better named condition 3'. and *replace* condition 3. from above definition?