LETHE: A Saturation-Based Tool for Non-Classical Reasoning

We present the saturation-based reasoning system Lethe. Lethe is a tool that can be used for uniform interpolation, forgetting, TBox abduction and logical di erence. To solve these problems, Lethe uses saturation-based reasoning to eliminate certain symbols from an ontology, such that entailments in the remaining vocabulary are preserved. This is known as forgetting or uniform interpolation. Lethe is an implementation of our forgetting methods for various expressive description logics, and can be used as a Java library and as a standalone tool for the mentioned reasoning tasks. We give a high level description of the calculi used by Lethe, describe the reasoning algorithm implemented in Lethe, and give an evaluation of the system on realistic ontologies.

[1]  Boris Konev,et al.  The Logical Difference Problem for Description Logic Terminologies , 2008, IJCAR.

[2]  Patrick Koopmann,et al.  Forgetting and Uniform Interpolation for ALC-Ontologies with ABoxes , 2014, Description Logics.

[3]  Boris Konev,et al.  Practical Uniform Interpolation and Forgetting for ALC TBoxes with Applications to Logical Difference , 2014, KR.

[4]  Carsten Lutz,et al.  Foundations for Uniform Interpolation and Forgetting in Expressive Description Logics , 2011, IJCAI.

[5]  Ian Horrocks,et al.  Consequence-Based Reasoning beyond Horn Ontologies , 2011, IJCAI.

[6]  Christopher G. Chute,et al.  BioPortal: ontologies and integrated data resources at the click of a mouse , 2009, Nucleic Acids Res..

[7]  Clare Dixon,et al.  Clausal resolution for normal modal logics , 2007, J. Algorithms.

[8]  Renate A. Schmidt,et al.  Forgetting Concept and Role Symbols in ALCOIHµ+(∇, ⊓)-Ontologies , 2016, IJCAI.

[9]  Clare Dixon,et al.  Clausal Resolution for Modal Logics of Confluence , 2014, IJCAR.

[10]  Grigori Mints,et al.  Gentzen-type systems and resolution rules. Part I. Propositional logic , 1990, Conference on Computer Logic.

[11]  Patrice Enjalbert,et al.  Modal Resolution in Clausal Form , 1989, Theor. Comput. Sci..

[12]  Yevgeny Kazakov,et al.  Consequence-Driven Reasoning for Horn SHIQ Ontologies , 2009, IJCAI.

[13]  P. Koopmann,et al.  Uniform Interpolation of ALC-Ontologies Using Fixpoints , 2013 .

[14]  Patrick Koopmann,et al.  Saturated-Based Forgetting in the Description Logic SIF , 2015, Description Logics.

[15]  Patrick Koopmann,et al.  Uniform Interpolation and Forgetting for ALC Ontologies with ABoxes , 2014, AAAI.

[16]  Boris Motik,et al.  Fixed Parameter Tractable Reasoning in DLs via Decomposition , 2011, Description Logics.