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RE: Expressiveness of RDF as Rule Conclusion Language (KIF or not to KIF)

From: Wagner, G.R. <G.R.Wagner@tm.tue.nl>
Date: Mon, 15 Oct 2001 12:22:04 +0200
Message-ID: <511BB18E82E9D11188230008C724064602D9DE1A@tmex1.tm.tue.nl>
To: "'Drew McDermott '" <drew.mcdermott@yale.edu>, "'www-rdf-rules@w3.org '" <www-rdf-rules@w3.org>
   [Gerd Wagner]
   Notice that we can associate a model-theoretic semantics with rules 
   in a natural way: an interpretation I satisfies a rule (is a model
   of it) if it satisfies its consequent whenever it satisfies its 
   antecedcent. 

   ... using the above definition of a model of a rule, we can 
   define that a rule set R entails a sentence F
   if all models of R satisfy F.

   [Drew McDermott]
   You're assuming that a what a rule set entails by your definition is
   equivalent to what is inferrable.  

I just explained that these two rules entail the sentence
'(status-known Joe)'. I didn't say anything about the inference
operation/engine to be used for processing them.

   [Drew McDermott]
   ... But the sort of rule in question here gives rise to 
   incompleteness for precisely the reasons you describe:
   '(status-known Joe)' is true in all models, but can't be inferred.
   This may be an argument against your proposed model-theoretic
   semantics for rules.

Why should the incompleteneness of some inference operation
(a less fundamental thing) be an argument against the underlying 
semantics (a more fundamental thing)? Also, what would be the
justification for an incomplete inference operation here? Don't 
we rather want the inference operation to be complete? And as 
you certainly know it is not a problem to find a complete 
inference operation for classical logic, so why not use such 
one, especially since KIF want to be classical, right?

   [Pat Hayes]  
   With this interpretation, the rule has exactly the same meaning 
   as the implication, indeed. So there would seem to be little 
   utility in making the distinction between rules and implications.

Why is this a question of utility? Implications are expressions
in the object language while rules are not. Indeed, the task
of an implication is to capture the meaning of a rule on the
object language level. And isn't it nice that implications 
(not just) in classical logic correspond pretty much to rules
(entail the same consequences as the corresponding rules)?  

   [Pat Hayes]  
   However, that is not the way that the KIF authors are intending 
   to use the term 'rule' 

But then they have a somewhat strange understanding of rules.

   [Pat Hayes]  
   Rules, in the sense used by the KIF authors, *are* a 
   proof-procedural matter: that is why they are called 'rules' 
   rather than, say, 'implications', you see, and why a notational
convention has been introduced into the syntax to state 
   them differently. 

Sure, the same holds for the concept of a sequent in Gentzen-style
calculi but still do these sequents satisfy the classical logic law 
of reasoning by cases, and they provide a complete inference
procedure wrt clasical logic. So, there is no point that rules
should not respect the law of classical logic just because their
purpose is to construct proofs.

   [Pat Hayes]  
   A rule is invoked only by an assertion. Neither of these rules 
   has a disjunction as an antecedent, so your argument is irrelevant. 
   You are confusing rules with material implications. 

I'm certainly not (wasn't it me who argued against you that they
are diferent concepts only recently on this list :-?)
If these rules are supposed to be (non-logical) rules in classical 
logic then they don't need a disjunction in their antecedent in
order to entail what is entailed in classical logic by the law
of reasoning by cases. You may intend them to be used in an 
incomplete inference operation, but as I have argued above, 
why would you want that we miss certain valid conclusions
that could be drawn if we just 'repair' the inference engine?

It seems to me that this is a confusion with the negation of
partial logic where the law of reasoning by cases does not hold,
and thus '(status-known Joe)' is not entailed, as in logic
programming. So, apparently, KIF wants to stay at the "safe"
side (classical logic) while at the same time it wants to use 
a negation that is more intuitive and cognitively adequate than 
classical negation. But such a balancing act is not possible!

Why is it so hard for many people to recognize that classical 
logic is not the proper logic for knowledge representation?

-Gerd
Received on Monday, 15 October 2001 06:22:33 GMT

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