- From: Sandro Hawke <sandro@w3.org>
- Date: Mon, 17 Sep 2001 10:56:52 -0400
- To: "Peter F. Patel-Schneider" <pfps@research.bell-labs.com>
- cc: G.R.Wagner@tm.tue.nl, www-rdf-rules@w3.org

> > Both with respect to bottom-up and to top-down evaluation it is > > natural then to define a derivation rule for a specific KR system > > in such a way that its antecedant is a query expression and its > > consequent is an input expression. > > Not to me it isn't. Again, there are lots of things in query languages > (like SQL) that we may not want in antecedants of rules. Similarly, there > may be things in rule consequents (e.g., variables) that we may not want in > the assertion language. > > Gerd Wagner > Peter F. Patel-Schneider I think we ought to seriously explore the possibility of using an RDF graph not only as the assertion language, but also as the query, rule- premise, and rule-conclusion languages. I'm sure it wont be perfect, but this seems like an important idea to consider and a strawman against which to compare alternatives. From here, I'd be interested to hear what you (Peter) think is still needed. Since I have trouble thinking in RDF graphs sometimes, I translate them to a small subset of FOL for this kind of work. Specifically, I use the subset with only constants, existential variables, 2-ary predicates, and conjunction. (No universal variables, no negation, no disjunction, no equality, and no logic functions.) Using this language for assertions is obvious. Using it for queries nearly obvious: you ask for a proof of the formula. Using it for a rule-premise or rule-conclusion gets a little more tricky, because we want to sort-of join the scopes of the existential variables in the two parts. I think there are two fairly natural ways to do this: one seems to give us datalog rules and the other seems to give us Horn rules. Style 1: Simply combine the scope of variables in the premise and conclusion. So if we have two RDF graphs (in FOL notation [2]): (1) EXISTS x In(Spot, x) AND In(x, TheYard) AND Material(x, Wood) (2) EXISTS x Isa(x, DogHouse) we can use these in a rule by turning the existential variables into universal variables in a scope outside of both formulas: FORALL x In(Spot, x) AND In(x, TheYard) AND Material(x, Wood) => Isa(x, DogHouse) I think this is as expressive as datalog. There is a question as to what it means if a variable occurs only in the second clause. In this style, I think we simply disallow that case. Style 2: We say that any variables in the second formula which are not also in the first formula remain as local existential variables. (1) EXISTS g1,g3 Grandparent(g1,g3) (2) EXISTS g1,g2,g3 Parent(g1,g2) AND Parent(g2,g3) would become a rule like this: FORALL g1,g3 Grandparent(g1,g3) => EXISTS g2 Parent(g1,g2) AND Parent(g2,g3) (This rule basically says that if two things have a grandparent relationship, there is a third thing and they have a transitive parent relationship through that third thing.) This may well not be full Horn logic, but I believe it's more expressive than Style 1, since I can't figure out how to express this example in Style 1. I also can't think of any Horn examples that I can't express in Style 2. (While Style 2 doesn't have the logic functions which normally separate datalog and Horn logic, the nested existential corresponds to Skolem functions, and in my playing around that seems to be enough. I don't have the skills to approach this formally.) (I have implemented Style 2, and I've talked about this before [1] but that discussion went in a somewhat different direction.) -- sandro [1] http://lists.w3.org/Archives/Public/www-rdf-logic/2001Mar/0075.html [2] I used an FOL ascii syntax found on this simple introduction: http://www.sdsc.edu/~tbailey/teaching/cse151/lectures/chap07a.html

Received on Monday, 17 September 2001 11:01:36 UTC