Reasoning with ontologies in Ontohub - Amazon AWS

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Reasoning with ontologies in Ontohub Eugen Kuksa Research group for theoretical computer science Institute for Intelligent Cooperating Systems (IKS) Otto-von-Guericke-Universität, Magdeburg, Germany

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Outline

1. Introduction 2. Ontohub Demo 3. Premise Selection 4. Conclusion

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Introduction

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Introduction: Problem

• You develop a large ontology • You need to make sure that it’s bug-free • You create competency questions • Reasoners run out of resources

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Introduction: Example

• Suggested Upper Merged Ontology (SUMO) • Problems with tens of thousands of axioms • Higher-Order Prover Leo-II runs into a timeout (60 seconds)

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Introduction: Solution

• Reduce the set of axioms for the reasoning task • Reasoning time decreases or reasoning even becomes possible at

all • The SUMO example passes after less than a second • The axiom set was reduced to 390 out of over 5000 axioms

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Ontohub

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Ontohub • Web application: https://ontohub.org • Repository for ontologies • Version control (git) • Integrated editor for small files • Analyses ontologies • Supports different logics • OWL • CommonLogic • TPTP (FOF, THF, etc.) • ... • Brings tool support • FaCT, Pellet • CVC4, Darwin, E-Prover, Geo-III, SPASS, Vampire • Leo-II, Satallax, Isabelle • ...

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Demo

• Create a repository • Upload an ontology • See its details • Run a reasoning task

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Premise Selection

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Premise Selection: General

• Produce a modified ontology • Modification is used only in the reasoner • If a proof is found, it is also a proof in the original ontology • If a counter example is found, we need to discard this result and

add axioms

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Premise Selection: The Algorithm ‘SInE’ • Developed by Krystof Hoder for SUMO • Fully automatic with a few user-defined parameters • Operates on syntax • Selects recursively the axioms that share a symbol with the

conjecture or an already selected axiom • The symbol that triggers the selection must hold more

conditions • Selection stops after n loops • Experiments with MPTP2078 show: 50% more problems can be

solved with SInE

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Premise Selection: Experimental Results (MPTP2078)

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Conclusion

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Conclusion

• Ontohub allows to • manage ontologies in repositories • develop ontologies with version control • make sure the ontologies are bug-free by using reasoners • Premise selection allows to find more proofs • SInE in Ontohub is only a prototype/proof of concept • More premise selection algorithms are being developed and will

be deployed to Ontohub

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References Krystof Hoder and Andrei Voronkov. Sine Qua Non for Large Theory Reasoning. In Automated Deduction - CADE-23 - 23rd International Conference on Automated Deduction, Wroclaw, Poland, July 31 - August 5, 2011. Proceedings, pages 299–314, 2011. Eugen Kuksa and Till Mossakowski. Ontohub: Version control, linked data and theorem proving for ontologies. In Oliver Kutz, Sergio de Cesare, Maria M. Hedblom, Tarek Richard Besold, Tony Veale, Frederik Gailly, Giancarlo Guizzardi, Mark Lycett, Chris Partridge, Oscar Pastor, Michael Grüninger, Fabian Neuhaus, Till Mossakowski, Stefano Borgo, Loris Bozzato, Chiara Del Vescovo, Martin Homola, Frank Loebe, Adrien Barton, and Jean-Rémi Bourguet, editors, JOWO@FOIS, volume 1660 of CEUR Workshop Proceedings. CEUR-WS.org, 2016. Eugen Kuksa and Till Mossakowski. Prover-independent axiom selection for automated theorem proving in ontohub. In PAAR@IJCAR, volume 1635 of CEUR Workshop Proceedings, pages 56–68. CEUR-WS.org, 2016. Till Mossakowski, Oliver Kutz, and Mihai Codescu. Ontohub: A semantic repository for heterogeneous ontologies. In Proc. of the Theory Day in Computer Science (DACS-2014), satellite workshop of ICTAC-2014, University of Bucharest, September 15-16, 2014, 2014.

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Thank you for listening! Questions?

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Premise Selection or Module Extraction?

Module extraction • is conservative – disproofs give knowledge • takes much longer • may yield ontologies that are too large

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