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Model Generation Theorem Proving for First-Order Logic OntologiesPowerPoint Presentation

Model Generation Theorem Proving for First-Order Logic Ontologies

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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

Model Generation for Ontologies

Our Contribution

Treating Equality

Achieving Termination

Evaluation

Model Generation Theorem Proving for FOL 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

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

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 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

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 comes in e.g.

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Model Generation Theorem Proving for FOL Ontologies

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

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1. Add equivalence axioms for =

2. Add predicate substitution axioms

3. Flatten the clauses

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

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still exponential)

Model Generation Theorem Proving for FOL Ontologies

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Model Generation Theorem Proving for FOL Ontologies

Cycles in Existential Roles

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Model Generation Theorem Proving for FOL Ontologies

Blocking Technique

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This search is encoded in the DLP (see paper for details).

Model Generation Theorem Proving for FOL Ontologies

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

Model Generation Theorem Proving for FOL Ontologies

Evaluation – W3C Benchmark Proofs for OWL

Model Generation Theorem Proving for FOL Ontologies

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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