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

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

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Krtzsch, Vrandecic, Hitzler, Sintek RuleML2006 Athens, GA November 2006 AIFB How to reason with OWL in a logic programming system Markus Krtzsch Denny Vrandecic AIFB Karlsruhe AIFB Karlsruhe Pascal Hitzler Michael Sintek

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Krötzsch, Vrandecic, Hitzler, Sintek ● RuleML2006 ● Athens, GA ● November ● 2006

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AIFB ReaSem

How to reason with OWL in a logic programming system

RuleML2006, Athens, GA November 2006 Markus Krötzsch AIFB Karlsruhe Pascal Hitzler AIFB Karlsruhe Denny Vrandecic AIFB Karlsruhe Michael Sintek DFKI Kaiserslautern

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Krötzsch, Vrandecic, Hitzler, Sintek ● RuleML2006 ● Athens, GA ● November ● 2006

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Semantic Web Languages: Seperate worlds

  • OWL DL

– open world – monotonic – description logics – first-order logic – decidable

  • Logic Programming

– closed world – non-monotonic – rules – procedural flavour – undecidable

  • both approaches are needed for applications
  • study of interoperability is imperative
  • here: sound and complete reasoning for OWL with Prolog
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Krötzsch, Vrandecic, Hitzler, Sintek ● RuleML2006 ● Athens, GA ● November ● 2006

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Approach

  • 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 Resolution and Deductive Databases. Dissertation, AIFB Universität Karlsruhe, 2006.

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Krötzsch, Vrandecic, Hitzler, Sintek ● RuleML2006 ● Athens, GA ● November ● 2006

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KAON2 Reasoner core architecture

SHIQ(D) TBox (no nominals) Transformation to Disjunctive Datalog [ExpTime] Query Disjunctive Datalog Reasoning Engine [coNP] SHIQ(D) ABox Answer

suffices for some queries e.g. instance retrieval for named classes

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Krötzsch, Vrandecic, Hitzler, Sintek ● RuleML2006 ● Athens, GA ● November ● 2006

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Theorem (Hustadt, Motik, Sattler 2004)

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.

  • 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).

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Krötzsch, Vrandecic, Hitzler, Sintek ● RuleML2006 ● Athens, GA ● November ● 2006

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Simple example transformation (ALC)

Q1(x), Person(y) ← parent(x,y) ← parent(x,y), Q1(y), Grandchild(x) ← Q1(x), Person(x) Grandchild(x)← Person(x) Person(a)

DD(KB) KB

Person v ∃ parent.Person ∃ parent.(∃ parent.Person) v Grandchild Person(a)

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Krötzsch, Vrandecic, Hitzler, Sintek ● RuleML2006 ● Athens, GA ● November ● 2006

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KAON2 Reasoner core architecture

OWL DL TBox (no nominals) Transformation to Disjunctive Datalog [ExpTime] Query OWL DL ABox Answer

suffices for some queries e.g. instance retrieval for named classes

Horn-SHIQ Disjunctive Datalog Reasoning Engine [coNP] [P]

: Horn-SHIQ

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Krötzsch, Vrandecic, Hitzler, Sintek ● RuleML2006 ● Athens, GA ● November ● 2006

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Horn-SHIQ

  • Fragment of OWL DL

– Polynomial data complexity (ABox) – ExpTime combined complexity (ABox+TBox) [OWLED06]

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Krötzsch, Vrandecic, Hitzler, Sintek ● RuleML2006 ● Athens, GA ● November ● 2006

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KAON2 Reasoner core architecture:

Transformation to Disjunctive Datalog [ExpTime] Query OWL DL ABox Answer

suffices for some queries e.g. instance retrieval for named classes

Horn-SHIQ Disjunctive Datalog Reasoning Engine [coNP] [P]

Horn-SHIQ

Prolog

Using Prolog

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Krötzsch, Vrandecic, Hitzler, Sintek ● RuleML2006 ● Athens, GA ● November ● 2006

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Difficulty: Integrity constraints

  • 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)

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Krötzsch, Vrandecic, Hitzler, Sintek ● RuleML2006 ● Athens, GA ● November ● 2006

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Difficulty: Equality

  • Some OWL statements require equality for

expressing them in first-order logic.

  • For our purposes, the following Horn rules suffice:
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Krötzsch, Vrandecic, Hitzler, Sintek ● RuleML2006 ● Athens, GA ● November ● 2006

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Example

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Krötzsch, Vrandecic, Hitzler, Sintek ● RuleML2006 ● Athens, GA ● November ● 2006

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Krötzsch, Vrandecic, Hitzler, Sintek ● RuleML2006 ● Athens, GA ● November ● 2006

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Implementation

Transformation available through KAON2 http://kaon2.semanticweb.org

  • r via owltools command line interface dlpconvert

http://owltools.ontoware.org see software demo [OWLED06] this evening – optional serialisations:

  • Prolog
  • F-Logic
  • RuleML0.9
  • SWRL
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Krötzsch, Vrandecic, Hitzler, Sintek ● RuleML2006 ● Athens, GA ● November ● 2006

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Acknowledgement

  • The presented results are corollaries from the work

by Boris Motik on KAON2.

  • Very helpful discussions with Boris are gratefully

acknowledged.

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Krötzsch, Vrandecic, Hitzler, Sintek ● RuleML2006 ● Athens, GA ● November ● 2006

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Thank you!

  • related [OWLED06]-presentations:

– Today, 1345 hrs:

  • M. Krötzsch, S. Rudolph and P. Hitzler. On the

Complexity of Horn Description Logics – Today, 1700 hrs:

  • D. Vrandecic: OWL Tools demo