1. Hitzler ● OWL1.1 Rules ● DedSys Saarbrücken ● March 2008 AIFB ReaSem Slide 1 OWL 1.1 Rules Markus Krötzsch Sebastian Rudolph Pascal Hitzler AIFB, University of Karlsruhe, Germany logic.aifb.uni-karlsruhe.de Deduktionstreffen, Saarbrücken, March 2008

2. Hitzler ● OWL1.1 Rules ● DedSys Saarbrücken ● March 2008 AIFB ReaSem Slide 2 Neuerscheinung Hitzler, Krötzsch, Rudolph, Sure Semantic Web – Grundlagen. Springer, 2008. 24,95 € Erstes deutsches Lehrbuch zu Grundlagen des Semantic Web. Behandelt u.a. Syntax, Semantik und Deduktionsverfahren von OWL ( SHOIN (D)).

3. Hitzler ● OWL1.1 Rules ● DedSys Saarbrücken ● March 2008 AIFB ReaSem Slide 3 Web Ontology Language OWL Semantic Web Knowledge Representation Language W3C recommendation April 2004. OWL DL: Fragment of 1 st order predicate logic. OWL DL: –Description Logic SHOIN (D). –decidable. –NExpTime

4. Hitzler ● OWL1.1 Rules ● DedSys Saarbrücken ● March 2008 AIFB ReaSem Slide 4 OWL1.1 Description Logic SROIQ in standardisation process (W3C) decidable, NExpTime-hard extends SHOIN with –role inclusion axioms R ± S v T –qualified number restrictions –punning –further role properties identified tractable fragments EL ++, DL-Lite, DLP, Horn- SHIQ,...

5. Hitzler ● OWL1.1 Rules ● DedSys Saarbrücken ● March 2008 AIFB ReaSem Slide 5 DL Rules Rules over some description logic L B, H sets of concept or role atoms in L, x the variables in B and H Rules of the form ( 8 x) B ! H with –for any non-initial individual u in B, there is a path from exactly one initial t to u in B –for any t,u there is at most one path in B from t to u –if H contains an atom C(t) or R(t,u), then t is initial in B V V

6. Hitzler ● OWL1.1 Rules ● DedSys Saarbrücken ● March 2008 AIFB ReaSem Slide 6 SROIQ Rules can be internalised into SROIQ internalisation is polynomial however, it is not an obvious transformation decidable fragment of SWRL within SROIQ

7. Hitzler ● OWL1.1 Rules ● DedSys Saarbrücken ● March 2008 AIFB ReaSem Slide 7 EL ++ Rules substantially extends EL ++ EL ++ together with EL ++ Rules are tractable (in P) EL ++ can be reduced to EL ++ Rules reduction is polynomial This allows to apply rule-based reasoning techniques for reasoning with EL ++ and EL ++ Rules!

8. Hitzler ● OWL1.1 Rules ● DedSys Saarbrücken ● March 2008 AIFB ReaSem Slide 8 DLP1.1 = DLP + DLP Rules Reducible to function-free first-order Horn rules with at most five variables per formula. Reduction can be done in polynomial time. DLP1.1 is tractable (in P)

9. Hitzler ● OWL1.1 Rules ● DedSys Saarbrücken ● March 2008 AIFB ReaSem Slide 9 Conclusions OWL1.1 Rules as expressive rules fragment of OWL1.1. Automatically supported by OWL1.1 reasoners. EL ++ Rules as new tractable fragment – includes EL ++. DLP1.1: new tractable rules fragment extending DLP.

10. Hitzler ● OWL1.1 Rules ● DedSys Saarbrücken ● March 2008 AIFB ReaSem Slide 10 More Details at the Poster! THANKS!