- From: Michael Kifer <kifer@cs.sunysb.edu>
- Date: Tue, 25 Apr 2006 10:56:01 -0400
- To: "Peter F. Patel-Schneider" <pfps@research.bell-labs.com>
- Cc: public-rif-wg@w3.org
> From: Michael Kifer <kifer@cs.sunysb.edu> > Subject: Re: [RIFWG] [Requirements?] A vision for the RIF > Date: Tue, 25 Apr 2006 09:28:12 -0400 > > > > > > 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". > > Why does the meaning of a KB always have to be a set of interpretations? > I meant bottom in the sense of "error", which is not a set of interpretations. I understood "bottom" to mean an "error". I just used your own definition to illustrate that for your example the meaning of both <S,C> and <C,S> is bottom. So, your definition is symmetric with respect to constraints and thus doesn't distinguish them from regular formulas. > > 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. > > Well, now, this is a different question. However, in fact, I do believe > that one could come up such a definition. It might not be pretty, and it > might not be completely stock FOL (e.g., it might require that constraints > be formulae, and talk about a substitution of names into constraints), but > it probably could be done. I'm not about to spend the effort, however, as > I think that an epistemic framework for constraints is better. Well, this was my main point. Whether epistemic or a form of CWA, it is not first-order. --michael
Received on Tuesday, 25 April 2006 15:11:03 UTC