Re: UPDATE: initial message concerning syntax

[...]

> Unfortunately, as I have already indicated in several places, this approach
> does not work, or, at best, only works with a lot of difficulty and
> fiddling.  To make it work correctly you have to include a full theory of
> lists and other syntactic constructions in your theory.  Once this is done,
> semantic paradoxes, or, if you prefer, the ability to derive a
> contradiction from the empty knowledge base, are very hard to avoid.
> Even if the whole formalism does not fail, there are quite a number of
> related issues that affect interpretations and inference.

I'm trying to agree with you, and it is indeed a possible
concern or, if you prefer, a challenge. We are currently
looking into "a theory of con-sequents in the presence of
inconsistencies" and I believe it could be engineered.
Anyhow, for the case of lists, I would be very interested
to see evidence for the problems that you mention, I mean
a test case or so. Our current entailment rules are
for all :x, :a, :b, :c

  ( :x / :b ) ont:item :x .
  { :b ont:item :x } log:implies { ( :a / :b) ont:item :x } .

  ( ( ) :x ) :append :x .
  { ( :a :b ) :append :c } log:implies { ( ( :x / :a ) :b ) :append ( :x / :c ) } .

but we still think about the entailment rules for a :schemaInconsistency

--
Jos De Roo, AGFA http://www.agfa.com/w3c/jdroo/