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 22:44:24 -0400
> 
> > 
> > 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.
> 
> Not so.  The meaning of <C,S> is the empty set of interpretations, a
> perfectly good value in the set of sets of interpretations, which is
> different from bottom, which is an "extra" possibility for the meaning of a
> KB. 
> 

I think you would have to change your definition in order for what you said
to be correct. According to what you wrote above, to have the meaning
"bottom" I need to show an interpretation, which satisfies every c \in C
(i.e., ~p(a)) but doesn't satisfy S (i.e., p(a)). Since, in fact, any
interpretation of C is such that S is not satisfied, the meaning is
"bottom".

That said, I should say that I admit the possibility that you might be able
to tweak your definition so that it will become asymmetric. But I doubt
that there is a "useful" sense (now I am being informal :-) in which
constraints can be defined in pure FOL.


	--michael

Received on Tuesday, 25 April 2006 13:28:30 UTC