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Deduktionstreffen 2005. Model Generation Theorem Proving for First-Order Logic Ontologies. Peter Baumgartner Fabian M. Suchanek. Max-Planck Institute for Computer Science Saarbrücken/Germany. Overview. Model Generation for Ontologies Our Contribution Treating Equality

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Deduktionstreffen 2005

Model Generation Theorem Proving

for First-Order Logic Ontologies

Peter Baumgartner

Fabian M. Suchanek

Max-Planck Institute for Computer Science Saarbrücken/Germany

Model Generation Theorem Proving for FOL Ontologies


Overview
Overview

Model Generation for Ontologies

Our Contribution

Treating Equality

Achieving Termination

Evaluation

Model Generation Theorem Proving for FOL Ontologies


Ontologies
Ontologies

Ontologies

OWL DL (Tambis, Wine, Galen)

OWL

FOL (SUMO/MILO, OpenCyc)

FrameNet

} DL-Provers

Reasoning Tasks

Satisfiability

Subsumption

Entailment

Instance retrieval

Model Generation Theorem Proving for FOL Ontologies


Ontologies1
Ontologies

Ontologies

OWL DL (Tambis, Wine, Galen)

OWL

FOL (SUMO/MILO, OpenCyc)

FrameNet

FOL Refutational Provers

Reasoning Tasks

Satisfiability

Subsumption

Entailment

Instance retrieval

Model Generation Theorem Proving for FOL Ontologies


Types of provers
Types of Provers

Shortcomings of Refutational Provers:

رThey often cannot produce models

(but models are useful as counterexamples or overviews)

ر They may not terminate on satisfiable formula sets

(but termination is highly desirable)

  • Proposal:

  • Use Model Generation Provers instead

Model Generation Theorem Proving for FOL Ontologies


Model generation provers
Model Generation Provers

Model Generation Provers compute models for satisfiable formula sets (iff the set is satisfiable and the prover terminates).

  • Existing Model Generation Provers include:

  • s-models

  • KRHyper (HyperTableaux)

  • Darwin (Model-Evolution)

Model Generation Theorem Proving for FOL Ontologies


Model generation for ontologies
Model Generation for Ontologies

Ontologies

OWL DL (Tambis, Wine, Galen)

OWL

FOL (SUMO/MILO, OpenCyc)

FrameNet

FOL

Clause Form

Reasoning Tasks

Satisfiability

Subsumption

Entailment

Instance retrieval

Model Generation Prover

Model

Model Generation Theorem Proving for FOL Ontologies


Equality
Equality

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Model Generation Theorem Proving for FOL Ontologies


Treating equality known approaches
Treating Equality – Known Approaches

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Approaches for treating equality

رNaive approach: Add the equality axioms

Problem: Cumbersome function substitution axioms

رBrand's Transformation (1975, later improved)

Works fine, but can be optimized in our case

Model Generation Theorem Proving for FOL Ontologies


Treating equality our approach
Treating Equality – Our Approach

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2. Add predicate substitution axioms

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A clause is flat iff all proper subterms are

constants or variables

Our transformation is complete and correct.

Model Generation Theorem Proving for FOL Ontologies


Treating equality comparison with brand
Treating Equality – Comparison with Brand

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Model Generation Theorem Proving for FOL Ontologies


Cycles in existential roles
Cycles in Existential Roles

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Model Generation Theorem Proving for FOL Ontologies


Cycles in existential roles1
Cycles in Existential Roles

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Model Generation Theorem Proving for FOL Ontologies


Blocking technique
Blocking Technique

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Model Generation Theorem Proving for FOL Ontologies


Blocking technique results
Blocking Technique – Results

Our blocking transformation

ر ensures termination in many cases

ر is complete and correct

ر can be applied to arbitrary formula sets (not just DL)

Model Generation Theorem Proving for FOL Ontologies


Evaluation consistency checks
Evaluation – Consistency Checks

Model Generation Theorem Proving for FOL Ontologies


Evaluation w3c benchmark proofs for owl
Evaluation – W3C Benchmark Proofs for OWL

Model Generation Theorem Proving for FOL Ontologies


Conclusion
Conclusion

Our approach for ontological reasoning

رproduces a model in case of satisfiability

ر can be applied to arbitrary ontologies (not just DL)

ر is competitive with existing systems

For details, see our paper

"Model Generation Theorem Proving for First-Order Logic Ontologies"

http://www.mpi-sb.mpg.de/~baumgart/publications/model-generation-ontologies.pdf

Model Generation Theorem Proving for FOL Ontologies


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