SWRL 0.6 A Semantic Web Rule Language Combining OWL and RuleML

1. SWRL 0.6A Semantic Web Rule Language Combining OWL and RuleML Ian Horrocks, Peter F. Patel-Schneider, Harold Boley, Said Tabet, Benjamin Grosof, Mike Dean presented by Axel Polleres http://www.daml.org/rules/proposal/

2. Overview • SWRL Overview • Abstract Syntax • Model-Theoretic Semantics • Not covered here: XML concrete Syntax/RDF concrete syntax • Usage Suggestions, why do we need rules? • Built-Ins • Decidability, why not?

3. SWRL Overview • Combines OWL DL + RuleML (basically: Horn Rules) • Straightforward combination  Decidability is lost! • Document defines Semantics and different Syntax proposals • Examples for rules and usage in the document

4. Abstract Syntax • Extends OWL DL abstract syntax by a further axiom: axiom ::= rule where rule ::= 'Implies(' [ URIreference ] { annotation } antecedent consequent ')' antecedent ::= 'Antecedent(' { atom } ')' consequent ::= 'Consequent(' { atom } ')' atom ::= description '(' i-object ')' | dataRange '(' d-object i-object ')' | individualvaluedPropertyID '(' i-object i-object ')' | datavaluedPropertyID '(' i-object d-object ')' | sameAs '(' i-object i-object ')' | differentFrom '(' i-object i-object ')' | builtIn '(' builtIn builtinID { d-object } ')' builtinID ::= URIreference Hmmm, typo? Only syntactic sugar, can be expressed by OWL

5. Abstract Syntax cont’d i-object ::= i-variable | individualID d-object ::= d-variable | dataLiteral i-variable ::= 'I-variable(' URIreference ')' d-variable ::= 'D-variable(' URIreference ')' • Basically, you can model Horn rules where atoms can be C(x), P(x,y), sameAs(x,y), differentFrom(x,y),or builtIn(r,x,...) where C is an OWL description or data range, P is an OWL property, r is a built-in relation, x and y are either variables, OWL individuals or OWL data values, as appropriate. • Safety (cf. Ullman) is required, i.e. vars in the head have to be bound in the body. no magic … we now use a more human readable syntax.

6. Semantics • As usual rules are satisfied by an interpretation if every variable binding satisfying the antecedent also satisfies the consequent. • Semantics of OWL unchanged, an interpretation • Satisfies an OWL ontology if all axioms (incl. rules) are satisfied. • No magic, no sophisticated semantics • BUT: decidability of either DL or Datalog alone is lost 

7. Where has all the decidability gone? • Problem: existential quantifiers + recursive rules… For instance (in DL syntax): C1(X) :- C2(X). C1 ⊑ ∃R.C2* C(a). by skolemization creates C(f(a)) C(f(f(a)) … etc. * Corresponds to a rule: (∃Y.R(X,Y)) :- C2(X) which amounts to ∀ X.∃Y.R(X,Y)) v not C2(X)

8. Where has all the decidability gone? Cont’d • The simple example from the last slide might still be solved with a blocking strategy in the evaluation algorithm, but… • … in general, interaction of existential quantifiers and recursive rules causes troubles, by introducing function symbols • It is not yet completely clear to me which SWRL “fragment” is fine…

9. State of discussion: • Which F-Logic fragment corresponds how to which SWRL fragment? (copied from deri-wsmo-discussion, thread: FvH> how weak must subsets of SWRL and FvH> pragmatic FLogic be before they start to diverge? MK> My guess is that they coincide on their pure Horn subsets and that MK> this is the maximal such subset. FvH> Thanks again for confirming this. I still think the rules must also be FvH> non-recursive for the two to coincide (from another point in your FvH> email, I think we agree on this). RV> Personally, I don't understand why rules have to be non-recursive. This RV> is definitely not the case for the DLP fragment. MK> I don't understand either. Why does recursion fall outside of the intersection of SWRL and F-logic? … MK> But in SWRL you can have recursion, no? RV> Yes. MK> So then recursion is in the intersection, I think. • Maybe Michael can comment on this further? • Reference for complexity & decidability of Logic Programming: Complexity and Expressive Power of Logic Programming , E. Dantsin, T. Eiter, G. Gottlob, and A. Voronkov TR version, 1999: http://www.kr.tuwien.ac.at/research/reports/rr9905.ps.gz Should be one of the next presentations probably in the DERI research seminar!

10. Conclusion & Outlook • Simple combination of DL and rules loses decidability. • Related works: • CARIN (Levy, Rousset, 1996) • Recent paper by Eiter et al. (KR 2004) • Description Logic Programs by Horrocks et al. (WWW 2003) • These works partly try to combine LP and DLs differently or impose syntactical restrictions for DL or for the rules.

11. Use for WSMO • F-Logic is FOL, thus undecidable… well, ok, semi-decidable. • F-Logic as in Flora is decidable but uses non-classical semantics, namely well-founded semantics for negation. • Use cases shall show which expressivity we need. • As long as we only use Horn-rules in F-Logic and don’t use function symbols, we are fine, since we don’t have existential introduction as in OWL, or no? • comments please! follow the discussions on the list… What are the next steps?