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

From: R.V.Guha <guha@guha.com>
Date: Mon, 21 Oct 2002 12:24:35 -0700
Message-ID: <3DB45473.9030403@guha.com>
To: Graham Klyne <GK@NineByNine.org>
CC: Pat Hayes <phayes@ai.uwf.edu>, RDF core WG <w3c-rdfcore-wg@w3.org>

Graham,

 Hope these responses help.

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?

Yes. This is because FOL is only semi-decidable.

>
> [[
> 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).

This follows from Godel's theorem ... not sure what your book means when 
it says that number theory is first order.

>
> [[
> 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.

Good point. Let me talk to Pat about this.

>
> [[
> 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]

Good point. We should clarify. We mean the former (i.e., identifier).

>
> 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?

Yes, it can be. So, as Quine pointed out, we don't need individuals.

>
> 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.

But variables *are* different ...

>
> 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.)

Good point.

>
> 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?
>
> ... 

I defer to Dan and Brian on this.

guha
Received on Monday, 21 October 2002 15:27:17 EDT

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