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

Peter F. Patel-Schneider <pfps@research.bell-labs.com> wrote:
>
> From: Michael Kifer <kifer@cs.sunysb.edu>
> Subject: Re: [RIFWG] [Requirements?] A vision for the RIF 
> Date: Mon, 24 Apr 2006 14:13:09 -0400
> 
> > 
> > > 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. 
> 
> Not so, my definition distinguishes between two things: bottom - which
> results from a constraint violation - and unsatisfiable - which is defined
> in the more-usual manner.
> 
> Consider a FOL version of the above 
> and look at S = { p(a) } and C = { ~p(a) }.  
> The meaning of < S , C > is bottom, because there are interpretations that
> satisfy p(a) but do not satisfy ~p(a).  
> The meaning of < S u C, {} > is the (empty) set of interpretations that
> satisfy both p(a) and ~p(a). 

And the meaning of <C,S> is also bottom. So, C and S are interchangeable,
which was exactly my point - there is no real difference between deductive
and normative formulas in FOL.


	--michael 


> > It is only when you depart from first-order semantics then you can
> > meaningfully distinguish constraints from deductive rules.
> 
> Not so, as evidenced by the formulation above.  
> 
> > 	--michael  
> 
> peter
>

Received on Tuesday, 25 April 2006 02:44:33 UTC