SWRL 0 6 A Semantic Web Rule Language

SWRL 0. 6 A Semantic Web Rule Language Combining OWL and Rule. ML Ian Horrocks, Peter F. Patel-Schneider, Harold Boley, Said Tabet, Benjamin Grosof, Mike Dean presented by Axel Polleres http: //www. daml. org/rules/proposal/ 1

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? 2

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

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 : : = Hmmm, typo? description '(' i-object ')' | data. Range '(' d-object i-object ')' | individualvalued. Property. ID '(' i-object ')' | datavalued. Property. ID '(' i-object d-object ')' | same. As '(' i-object ')' Only syntactic sugar, | different. From '(' i-object ')' can be expressed by OWL | built. In '(' built. In builtin. ID { d-object } ')' builtin. ID : : = URIreference 4

Abstract Syntax cont’d i-object d-object i-variable : : = d-variable : : = • • : : = i-variable | individual. ID d-variable | data. Literal 'I-variable(' URIreference ')' 'D-variable(' URIreference ')' Basically, you can model Horn rules where atoms can be C(x), P(x, y), same. As(x, y), different. From(x, y), or built. In(r, x, . . . ) where C is an OWL description or data range, P is an OWL property, r is a builtin 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. 5

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 6

Where has all the decidability gone? • Problem: existential quantifiers + recursive rules… For instance (in DL syntax): C(a). C 1(X) : - C 2(X). C 1 ⊑ ∃ R. C 2* by skolemization creates C(f(a)) C(f(f(a)) … etc. * Corresponds to a rule: (∃Y. R(X, Y)) : - C 2(X) which amounts to ∀ X. ∃Y. R(X, Y)) v not C 2(X) 7

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… 8

State of discussion: • Which F-Logic fragment corresponds how to which SWRL fragment? (copied from deri-wsmo-discussion, thread: Fv. H> how weak must subsets of SWRL and Fv. H> 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. Fv. H> Thanks again for confirming this. I still think the rules must also be Fv. H> non-recursive for the two to coincide (from another point in your Fv. H> 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/rr 9905. ps. gz Should be one of the next presentations probably in the DERI research seminar! 9

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. 10

Use for WSMO • F-Logic is FOL, thus undecidable… well, ok, semidecidable. • F-Logic as in Flora is decidable but uses nonclassical 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? 11