How to reason with OWL in a logic programming system Markus Krtzsch - PowerPoint PPT Presentation

Krötzsch, Vrandecic, Hitzler, Sintek ● RuleML2006 ● Athens, GA ● November ● 2006 AIFB How to reason with OWL in a logic programming system Markus Krötzsch Denny Vrandecic AIFB Karlsruhe AIFB Karlsruhe Pascal Hitzler Michael Sintek ReaSem AIFB Karlsruhe DFKI Kaiserslautern RuleML2006, Athens, GA November 2006 Slide 1

Krötzsch, Vrandecic, Hitzler, Sintek ● RuleML2006 ● Athens, GA ● November ● 2006 Semantic Web Languages: Seperate worlds AIFB • OWL DL • Logic Programming – open world – closed world – monotonic – non-monotonic – description logics – rules – first-order logic – procedural flavour – decidable – undecidable • both approaches are needed for applications ReaSem • study of interoperability is imperative • here: sound and complete reasoning for OWL with Prolog Slide 2

Krötzsch, Vrandecic, Hitzler, Sintek ● RuleML2006 ● Athens, GA ● November ● 2006 Approach AIFB • We utilize results by Motik et al. on the KAON2 transformation algorithms and system. • KAON2 OWL reasoner: http://kaon2.semanticweb.org • KAON2 algorithms comprehensive details: Boris Motik, Reasoning in Description Logics using ReaSem Resolution and Deductive Databases. Dissertation, AIFB Universität Karlsruhe, 2006. Slide 3

Krötzsch, Vrandecic, Hitzler, Sintek ● RuleML2006 ● Athens, GA ● November ● 2006 KAON2 Reasoner core architecture AIFB SHIQ(D) TBox Query SHIQ(D) ABox (no nominals) suffices for some queries Transformation to e.g. instance retrieval for Disjunctive Datalog named classes [ExpTime] ReaSem Disjunctive Datalog Reasoning Engine [coNP] Answer Slide 4

Krötzsch, Vrandecic, Hitzler, Sintek ● RuleML2006 ● Athens, GA ● November ● 2006 Theorem (Hustadt, Motik, Sattler 2004) AIFB Transformation of OWL knowledge base KB into Disjunctive Datalog DD(KB) Then, the following hold: 1. KB is unsatisfiable if and only if DD(KB) is unsatisfiable. 2. KB ² α if and only if DD(KB) ² α , where α is of the form A(a) or R(a, b), and A is an atomic concept. ReaSem 3. KB ² C(a) for a nonatomic concept C if and only if, for Q a new atomic concept, DD(KB ∪ {C v Q}) ² Q(a). Slide 5

Krötzsch, Vrandecic, Hitzler, Sintek ● RuleML2006 ● Athens, GA ● November ● 2006 Simple example transformation (ALC) AIFB KB Person v ∃ parent.Person ∃ parent.( ∃ parent.Person) v Grandchild Person(a) DD(KB) Q 1 (x), Person(y) ← parent(x,y) ← parent(x,y), Q 1 (y), Grandchild(x) ReaSem ← Q 1 (x), Person(x) Grandchild(x) ← Person(x) Person(a) Slide 6

Krötzsch, Vrandecic, Hitzler, Sintek ● RuleML2006 ● Athens, GA ● November ● 2006 KAON2 Reasoner core architecture : Horn-SHIQ AIFB OWL DL TBox Horn-SHIQ OWL DL ABox Query (no nominals) suffices for some queries Transformation to e.g. instance retrieval for Disjunctive Datalog named classes [ExpTime] ReaSem Disjunctive Datalog Reasoning Engine [coNP] [P] Answer Slide 7

Krötzsch, Vrandecic, Hitzler, Sintek ● RuleML2006 ● Athens, GA ● November ● 2006 Horn-SHIQ AIFB • Fragment of OWL DL – Polynomial data complexity (ABox) – ExpTime combined complexity (ABox+TBox) [OWLED06] ReaSem Slide 8

Krötzsch, Vrandecic, Hitzler, Sintek ● RuleML2006 ● Athens, GA ● November ● 2006 KAON2 Reasoner core architecture: Horn-SHIQ Using Prolog AIFB Horn-SHIQ OWL DL ABox Query suffices for some queries Transformation to e.g. instance retrieval for Disjunctive Datalog named classes [ExpTime] ReaSem Disjunctive Datalog Reasoning Engine [coNP] [P] Prolog Answer Slide 9

Krötzsch, Vrandecic, Hitzler, Sintek ● RuleML2006 ● Athens, GA ● November ● 2006 Difficulty: Integrity constraints AIFB • Some OWL statements become integrity constraints which are not usually supported under Prolog. • C u D ≡ ⊥ translates to ← C(x) ∧ D(x) • workaround: inc ← C(x) ∧ D(x) ReaSem Slide 10

Krötzsch, Vrandecic, Hitzler, Sintek ● RuleML2006 ● Athens, GA ● November ● 2006 Difficulty: Equality AIFB • Some OWL statements require equality for expressing them in first-order logic. • For our purposes, the following Horn rules suffice: ReaSem Slide 11

Krötzsch, Vrandecic, Hitzler, Sintek ● RuleML2006 ● Athens, GA ● November ● 2006 AIFB Example ReaSem Slide 12

Krötzsch, Vrandecic, Hitzler, Sintek ● RuleML2006 ● Athens, GA ● November ● 2006 AIFB ReaSem Slide 13

Krötzsch, Vrandecic, Hitzler, Sintek ● RuleML2006 ● Athens, GA ● November ● 2006 Implementation AIFB Transformation available through KAON2 http://kaon2.semanticweb.org or via owltools command line interface dlpconvert http://owltools.ontoware.org see software demo [OWLED06] this evening – optional serialisations: • Prolog ReaSem • F-Logic • RuleML0.9 • SWRL Slide 14

Krötzsch, Vrandecic, Hitzler, Sintek ● RuleML2006 ● Athens, GA ● November ● 2006 Acknowledgement AIFB • The presented results are corollaries from the work by Boris Motik on KAON2. • Very helpful discussions with Boris are gratefully acknowledged. ReaSem Slide 15

Krötzsch, Vrandecic, Hitzler, Sintek ● RuleML2006 ● Athens, GA ● November ● 2006 AIFB Thank you! • related [OWLED06]-presentations: – Today, 1345 hrs: M. Krötzsch, S. Rudolph and P. Hitzler. On the Complexity of Horn Description Logics ReaSem – Today, 1700 hrs: D. Vrandecic: OWL Tools demo Slide 16