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Re: Comments/questions on lBase (ACTION 2002-10-18#1)

From: Dan Brickley <danbri@w3.org>
Date: Mon, 21 Oct 2002 13:53:02 -0400 (EDT)
To: Graham Klyne <GK@NineByNine.org>
cc: <w3c-rdfcore-wg@w3.org>
Message-ID: <Pine.LNX.4.30.0210211350580.12502-100000@tux.w3.org>


graham,

any chance you could split these between issues that you feel ought to
be responded to before we push out a Note, and things for subsequent
consideration?

thanks for taking the time to review this,

Dan

On Mon, 21 Oct 2002, Graham Klyne wrote:

>
> Section 2.1:
>
> I don't understand this bit:
> [[
> Mapping type/class language into predicate/application language also
> ensures that set-theoretical paradoxes do not arise.
> ]]
>
> I think this section is saying that it may be ultimately not possible to
> detect inconsistencies in statements made in different SWEL's mapped onto
> lBase, but that in practical terms it should be possible to detect most
> such inconsistencies.  Is this about right?
>
> [[
> Numerals are defined to be strings of the characters '0123456789', and are
> interpreted as decimal numerals in the usual way. Since arithmetic is not
> first-order definable, this is the first and more obvious place that Lbase
> goes beyond first-order expressiveness.
> ]]
> Dumb question:  how is arithmetic different from number theory?  In
> particular, I understood that (elementary) number theory was first-order
> (or: that's what my book says).
>
> [[
> Any Lbase language is defined with respect to a vocabulary, which is a set
> of non-special names. We require that every Lbase vocabulary contain all
> urirefs, but other expressions are allowed. (We will require that every
> Lbase interpretation provide a meaning for every special name, but these
> interpretations are fixed, so special names are not counted as part of the
> vocabulary.)
> ]]
> I think I see where this is going, but I'm not sure I could explain
> it.  This may need a little further explanation if the intended audience is
> not just logicians (particularly the idea about special names having fixed
> interpretations, and vocabulary not).  Or, depending on your intended
> audience, this may be fine -- in which case I'd suggest indicating up-front
> what you believe to be the audience for this document.
>
> [[
> We do not take any position here on the way that urirefs may be composed
> from other expressions, e.g. from relative URIs or Qnames; the model theory
> simply assumes that such lexical issues have been resolved in some way that
> is globally coherent, so that a single uriref can be taken to have
> the  same meaning wherever it occurs.
> ]]
> There is a message that Tim Berners-Lee posted to the www-tag list recently
> [1], which for me clarified an important difference between the intended
> roles of URIs and URI references (specifically, calling out the roles of
> *identifiers* and *references*).
>
> [1] http://lists.w3.org/Archives/Public/www-tag/2002Sep/0043.html
> [[
> It is important to distinguish between the string which identifies
> something and the BNF for a string in a document which
> is used to specify the first string.  The first is an identifier.
> The second has been called a "reference".   A reference
> can use a relative form.
> ]]
> - from [1]
>
>
> Section 2.2
>
> A nit.  You say:
> [[
> We will assume that there are three sets of names (not special names) which
> together constitute the vocabulary: individual names, relation names, and
> function names, and that each function name has an associated arity, which
> is a non-negative integer. In a particular vocabulary these sets may or may
> not be disjoint.
> ]]
> Can a function have zero arity (zero being non-negative)?
> If so, how would that differ from an individual?
>
>
> Section 2.3:
>
> Para 2, typo?:
> [[
> In specifying the following it is convenient to define use some standard
> definitions.
> ]]
>
> I think the definition of function is missing something.  I couldn't follow
> it, though I think I know where it intends to finish.  I think something
> like "for any value s0 for which R has an element <s0,s1,...,sn>, if there
> is exactly one such element of R, then..."?
>
> I'm puzzled why variables have a special status in the syntax.  As far as I
> can tell (so far), they are treated just like other names, except that
> quantifier-bound variables must have the syntactic form of a variable.  I'm
> thinking this could go one of two ways:
> (a) don't allow variable names except as quantified values, or
> (b) allow any name to be quantified, and note a convention that ?name form
> is used for this purpose.
>
> Question:  as it stands, the definition of interpretation seems to require
> a denotation for any variable, even though it may appear only bound in a
> quantifier;  e.g. in:
>
>     (forall (?x) R(?x) )
>
> the denotation of ?x given by an interpretation seems pretty irrelevant.  I
> suppose one could always include a Herbrand-style mapping for such
> elements, but this feels to me as if it adds a small unnecessary complication.
> [I see you come to this point later.]
>
> There is a condition on I that refers to function symbols, but it's not
> clear to me that there is any way to distinguish a function symbol from any
> other name, so I'm not sure what purpose the condition serves.
>
> I presume "I(A)=I(B)" means that I(A) and I(B) are the same member of
> ID+ISN?  (Maybe this should be obvious, but I've just been reading
> elsewhere about variations of URI equality, and I'm feeling a little confused.)
>
> If E is:  a term f(t1,...,tn),
> what is the value of I(E) when IEXT(I(f)) is not functional?
> It seems to me that such a term cannot be excluded from a wff as the
> functional property of IEXT(I(f)) is determined by the interpretation, not
> the expression.
> I think this must be bound up with my earlier question about functional
> symbols and conditions on an interpretation...
>
> Is the concept of a "knowledge base" really useful, given lBase's role as a
> specification language and the fact that the same effect is achieved by
> Boolean conjunction formula?
>
> I liked the presentation of axiom schemes.  For me that justified something
> that I'd previously seen as handwaving to be taken on faith.
>
>
> Section 3.0:
>
> Is it also needed to provide some indication of which vocabulary items
> introduced by Li may be used as functions?  (See above comments about
> functions.)
>
>
> Section 3.1:
>
> The indicated diagrams do not show up in my browser (Opera).
>
> (This is probably because I'm reviewing the mail archive copy, not using a
> directly published URI.)
>
>
> Section 6.0:
>
> When we publish this as a WG NOTE, would it not be more appropriate to
> reference the other documents of this WG rather than the older RDF documents?
>
> ...
>
> That completes my contribution to ACTION 2002-10-18#1
>
> #g
>
>
> -------------------
> Graham Klyne
> <GK@NineByNine.org>
>
Received on Monday, 21 October 2002 13:53:04 EDT

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