Re: RDF Semantics: presenting the definition of rdfs interpretations

  Hi Herman

I will take these as editorial comments on the semantics document, 
and respond directly.

>Some time ago we had a long discussion on rdf-comments
>on the question where to put the definition of IC and ICEXT [1].
>You defended your "table-definitive policy", which
>includes the definition of these items in the table in Section 3.3
>of the RDF Semantics document.
>I proposed to take the definition of IC and ICEXT before the
>table.  Then, the table would become simpler, since it would
>not use new terminology, and there would be no forward reference.
>(By the way, you never said why you wanted the table-definitive

Partly for aesthetic reasons, partly so that the entire MT can be 
captured unambiguously in equations by simply merging the tables.  My 
own view is basically that an MT actually *is* a set of equations, 
strictly speaking, and the rest of the text is just commentary, 
introduction etc. for the benefit of various categories of human 
reader. But some readers can do best with simply the equations.

>At first I was happy with your adaptation of the table-definitive
>text, but I am afraid I now want to discuss the point further.
>I have two excuses for this: 1) the definition of rdfs interpretation
>is undoubtedly the most complicated thing in the RDF Semantics document,
>so it is valuable to make it as simple as possible.

I agree

>2) Peter Patel-Schneider pointed to an interpretation of the new editor's
>version text which is clearly undesirable.  You said earlier that
>you view IC and ICEXT as add-ons, and not (as fundamental as for example
>IP and IEXT) as part of the definition of RDFS interpretation.
>However, the new text
>  >       An rdfs-interpretation of V is an rdf-interpretation
>>        I of (V union rdfV union rdfsV) *with a distinguished subset IC
>>        of the universe and a mapping ICEXT from IC to the set of
>  >       subsets of IR*, which ...
>allows the confusion that IC and ICEXT are part of the tuple
>that forms an rdfs-interpretation.
>This view would be undesirable.

I tend to agree, for the reasons you give below, but I have not 
stated that they are; the text currently (quoted above) states 
unambiguously, it seems to me, that an rdfs-interpretation *is* an 
rdf-interpretation.  A named set with a distinguished named subset is 
still a named set.

>  It would be simplest if
>each semantic extension of simple interpretations (rdf interpretations,
>rdfs interpretations, owl full interpretations, owl dl interpretations
>etc.) would still be the same kinds of 6-tuples, with more and more
>conditions being satisfied.

Quite; that is why I chose that form of words.

>Otherwise, for example, the OWL semantics document
>would need to reconsider each of the many uses of rdfs-interpretation.
>And even within the RDF Semantics document the interpretation that
>IC and ICEXT are part of an rdfs interpretation seems to lead to problems
>of presentation.  For example, the rdfs closure lemma would
>need a somewhat awkward reformulation: the Herbrand interpretation of the
>rdfs closure of E (this is a simple interpretation - no IC and
>ICEXT yet) is (subinterpretation of) an rdfs-interpretation of E
>(where did IC and ICEXT come from?)
>In view of this, I propose something like the following simplification
>of the text defining rdfs interpretations.

Your text, below, seems to me to be considerably more complicated 
than the current text.

>This is a slight adaptation
>of text that was proposed by Peter.  The following text seems to be
>make it completely equivalent to what is now in the editor's version
>(26 February), apart from the confusion about the position of IC and
>         An rdfs-interpretation of V is an rdf-interpretation I of (V union
>         rdfV union rdfsV) which satisfies the following semantic
>         and all the triples in the subsequent table, called the RDFS
>         axiomatic triples.  For convenience, and to make the semantic
>         conditions easier to understand,
>         the set of classes IC is defined as
>                 IC = { y in IR | <y,I(rdfs:Class)> is in IEXT(I(rdf:type))
>       and the function ICEXT from IC into the powerset of IR is
>       defined, for each x in IC, as
>                 ICEXT(x) = { y in IR | <y,x> is in IEXT(I(rdf:type)) }.
>         These definitions imply that
>             IP = ICEXT(I(rdf:Property))
>                 IC = ICEXT(I(rdfs:Class)).
>The other discussion of IC and ICEXT before the definition of
>an rdfs-interpretation could then (largely) be removed.
>And the first and second conditions could be deleted from the table.

I do not wish to remove anything from the table which would render 
the tables alone (without any surrounding text) incomplete as a 
specification of the semantics, so they must somehow contain these 
definitions or something which is equivalent to these definitions. At 
present this amounts to two lines:

x is in ICEXT(y) iff <x,y> is in IEXT(I(rdf:type))

IC = ICEXT(I(rdfs:Class))

which are the first two items in the table.

Again, this seems to me to be considerably simpler (both in terms of 
length, and also easier to understand) than your proposed text.

If you wish, I could make the following addition to the above quoted text:

  "An rdfs-interpretation of V is an rdf-interpretation I of (V union 
rdfV union rdfsV) with a distinguished subset IC of the universe and 
a mapping ICEXT from IC to the set of  subsets of IR, which satisfies 
the following semantic conditions and all the triples in the 
subsequent table, called the RDFS axiomatic triples. [Note that the 
interpretations of ICEXT, and hence of IC, are fixed in any 
rdf-interpretation by the interpretation of IEXT(I(rdf:type)).]

Would this be helpful?

>These changes would make the document somewhat shorter and the definition
>of rdfs interpretations simpler: there would be no forward reference

There never has been any forward reference, other than by way of 
explanatory text introducing a new concept before giving the precise 
account, which I feel is not only normal practice but if anything 
desirable in a document of this kind with this intended audience.

>, and the table does no longer make use of any new terminology.

? But it does: this table and all the subsequent tables use the 
IC/ICEXT language extensively. If the tables contain nothing to 
define them then they are effectively undefined.

>With this mail, I retract my previous reply [1], to which you have not

A reply would have been forthcoming eventually, but here is what it 
would have said, in brief:

1. The insertion of the "If x is in IR and y is in IC, then " 
precondition is inappropriate (since this equation is intended to 
apply without restriction) and unnecessary.

2. The insertion of "for x in IC" as a precondition in the text is 
unnecessary since the range of rdf:type is rdfs:Class, and this text 
is intended only to be an introductory aid to intuition in any case.

>and which does not seem to have had effect on the editor's
>version of the RDF Semantics document.

See above.

>Herman ter Horst


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Received on Thursday, 10 April 2003 14:41:34 UTC