Re: [RIFWG] [Requirements?] A vision for the RIF

> From: Michael Kifer <kifer@cs.sunysb.edu>
> Subject: Re: [RIFWG] [Requirements?] A vision for the RIF 
> Date: Mon, 24 Apr 2006 12:15:24 -0400
> 
> > 
> > 
> > > Michael Kifer wrote:
> > > > I said that normative rules imply that we must use some sort of a closed
> > > > world assumption. Under the open-world assumption there is no useful way to
> > > > distinguish between normative rules and deductive rules, but under the CWA
> > > > there is.
> > > >   
> > > 
> > > I am not sure I can agree with this. I can very well imaginbe normative
> > > rules not governed by a Closed World Assumption.
> > 
> > Francois,
> > 
> > The above must be taken in the context of my earlier message
> > http://lists.w3.org/Archives/Public/public-rif-wg/2006Mar/0161.html
> > where I *proved* that the rule set for which those normative rules act as
> > constraints must have some sort of closed world assumption (more precisely,
> > cannot use the normal first-order semantics).
> > 
> > I did not say that normative rules must be "governed" by CWA, because I
> > don't know what this might mean.
> > 
> > If you think that my very short proof has a bug then please point this out.
> > 
> > 	--michael  
> 
> I'm not sure why it is necessary for constraints to be interpreted in a CWA
> environment.
> 
> In particular, I don't see why the following development is not suitable:
> 
> Given a logical language (e.g., FOL or Horn rules), consisting of a syntax
> 	for axioms (e.g., FOL statements or ground atomic facts plus Horn
> 	rules) in the language and a model-theoretic semanticsbased on a
> 	set of interpretations and a primitive satisfaction relationship
> 	written i |= a, with i an interpretation and a an axiom (e.g.,
> 	Tarskian FOL semantics or some minimal-model semantics for Horn
> 	rule).
> 
> Let a KB = < S, C > be a pair of two sets of axioms (the statements and
> 	the constraints of the KB) 
> 
> Define the meaning of a KB = < S, C > as
>  	bottom if there is some interpretation i that satisfies each s in S
>                but there is some c in C where i does not satisfy c;
> 	{ i | i |= s for all s in S } otherwise
> 
> Yes, this is not what LP people think of as their way of working with
> constraints, but I don't see why it is not an acceptable way of thinking
> about constraints.
> 
> peter
> 

Because you defined precisely the set of models of S union C. Right?
That is, there is no difference between S and C whatsoever. This was
precisely my point.
Under FO semantic, there is no difference between deduction and
constraints and the distinction is completely arbitrary.
You might as well call S "normative" and C "deductive" or
S union C "normative" or "deductive", or both. 

It is only when you depart from first-order semantics then you can
meaningfully distinguish constraints from deductive rules.


	--michael

Received on Monday, 24 April 2006 18:13:16 UTC