From: Wagner, G.R. (G.R.Wagner@tm.tue.nl)
Date: 04/26/03
Benjamin, some quick comments to your > Approaches to Negation in RuleML > V1 draft 4/25/2003 You say that > NAF is the most commonly used form of negation in > commercially important rule systems, i.e in Prolog, SQL, > OPS5 production rules, ECA rules. Notice that in SQL, and also in UML/OCL, the "official" negation is neither NAF nor Boolean (2-valued), but rather Kleene's 3-valued (also called "strong") negation. In addition to this strong negation, there is also NAF, e.g. in the from of the EXCEPT operation. I have a preliminary report on this at http://tmitwww.tm.tue.nl/staff/gwagner/myRuleML/SemWebNeg.pdf > The large majority of the knowledgeable LP R&D community, > prefers/recommends the well-founded semantics (WFS) How do you know there is such a majority, was there any vote? I'd like to remark that the well-founded semantics is not a logical semantics in the classical model-theoretic sense, but rather a proof procedure/theory based on certain intuitive principles of constructing inferences, which do, however, not apply to the more general case of disjunctive logic programs, as there is no unique generalization of WFS to disjunctive rules. This shows that well-founded inference is a sound but incomplete proof calculus with respect to the stable model semantics (which applies both to normal and disjunctive rules). > It uses a third truth value -- "u" for "undefined" -- for > the nastily oscillatory cases of cyclic dependence This is an unfortunate use of a third truth value for something where, in fact, no third truth value is needed: these "oscillatory cases of cyclic dependence" correspond to undecidability in the sense that neither the atom nor its negation is provable - but that's not a case where you need a third truth value; using a third truth value for this purpose is like using a sledge hammer to crack a nut. Notice that you do need a third truth value, however, as soon as you introduce a second negation, like in "extended logic programs" (simply because two truth value allow only for one negation). > Let us call the strong-negation operator "cneg" or "not", > and the NAF operator "fneg" or "fail". In previous RuleML discussions we used to calle these two negations "neg" and "naf", which seems to be more user- friendly. > The first, and most basic, aspect of the semantic treatment > of strong negation is to view "cneg p", where p is any > predicate, as equivalently standing for another "not_p", > where "not_p" is a newly introduced predicate. Intuitively, > what is going on is that one reasons *separately* about > both "sides" (positive and strong-negative) of each > predicate "p". This is not quite true, because even if one does not enforce the law of the excluded middle for "cneg", one does want to enforce the law of the excluded contradiction, so one would have to make sure that "not_p" excludes "p" (as it is done in the semantics of extended logic programs). The most general logical treatment of rules with two kinds of negation, as far as I know, is http://tmitwww.tm.tue.nl/staff/gwagner/PartialLogics.pdf published in D.M. Gabbay and H. Wansing (Eds.), What is Negation?, Kluwer Academic Publishers, 1999. I agree that, ultimately, some form of inconsistency tolerance is needed in an expressive Web rule language, and your proposal of "Courteous LP" seems to be an interesting candidate for this, but "politically/psychologically" it is more advisable to postpone this issue until the more basic issues have been settled (many people, especially in the "logicist AI" tradition, are scared by the issue of inconsistency tolerance). Best, G e r d --------------------------------------- Gerd Wagner http://tmitwww.tm.tue.nl/staff/gwagner/ Dep. Information & Technology Eindhoven University of Technology Email: G.Wagner@tm.tue.nl Phone: (+31 40) 247 26 17 Fax: (+31 40) 247 26 12
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