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

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 08:44:05 UTC