Forgetting Concept and Role Symbols in ALCOIH\mu+(\top, \sqcap)-Ontologies

Forgetting is a non-standard reasoning problem that is concerned with creating restricted views of ontologies relative to a subset of the initial signature and preserving pertinent logical consequences up to the symbols in the restricted views. In this paper, we present an Ackermann-based approach for forgetting of concept and role symbols in ontologies expressible in the description logic ALCOIHμ(O,u). The method is one of only few approaches that can eliminate role symbols, that can handle role inverse and ABox statements (via nominals), and the only approach so far providing support for forgetting in description logics with nominals. Despite the inherent difficulty of forgetting for this level of expressivity, performance results with a prototypical implementation have shown very good success rates on real-world ontologies.

[1]  W. Ackermann.  Untersuchungen über das Eliminationsproblem der mathematischen Logik , 1935 .

[2]  Dov M. Gabbay,et al.  Second-Order Quantifier Elimination - Foundations, Computational Aspects and Applications , 2008, Studies in logic : Mathematical logic and foundations.

[3]  Patrick Koopmann,et al.  Count and Forget : Uniform Interpolation of SHQ-Ontologies — Long Version ? , 2014 .

[4]  Jeff Z. Pan,et al.  ELIMINATING CONCEPTS AND ROLES FROM ONTOLOGIES IN EXPRESSIVE DESCRIPTIVE LOGICS , 2014, Comput. Intell..

[5]  Jeff Z. Pan,et al.  Forgetting Concepts in DL-Lite , 2008, ESWC.

[6]  Boris Konev,et al.  Model-theoretic inseparability and modularity of description logic ontologies , 2013, Artif. Intell..

[7]  Andreas Herzig,et al.  Uniform Interpolation by Resolution in Modal Logic , 2008, JELIA.

[8]  Dov M. Gabbay,et al.  Quantifier Elimination in Second-Order Predicate Logic , 1992, KR.

[9]  Patrick Doherty,et al.  Computing Circumscription Revisited: A Reduction Algorithm , 1997, Journal of Automated Reasoning.

[10]  Sebastian Rudolph,et al.  (Non-)Succinctness of uniform interpolants of general terminologies in the description logic EL , 2014, Artif. Intell..

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

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

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

[14]  A. Visser.  Bisimulations, model descriptions and propositional quantifiers , 1996 .

[15]  Renate A. Schmidt,et al.  Using tableau to decide description logics with full role negation and identity , 2012, ACM Trans. Comput. Log..

[16]  Jeff Z. Pan,et al.  Forgetting for knowledge bases in DL-Lite , 2010, Annals of Mathematics and Artificial Intelligence.

[17]  Giuseppe De Giacomo,et al.  Reasoning in Expressive Description Logics with Fixpoints based on Automata on Infinite Trees , 1999, IJCAI.

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

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

[20]  Renate A. Schmidt,et al.  Concept Forgetting for ALCOI-Ontologies using an Ackermann Approach , 2015, Description Logics.

[21]  Jeff Z. Pan,et al.  Concept and Role Forgetting in ALC Ontologies , 2009, ISWC 2009.

[22]  Igor Walukiewicz,et al.  Guarded fixed point logic , 1999, Proceedings. 14th Symposium on Logic in Computer Science (Cat. No. PR00158).

[23]  Boris Konev,et al.  Forgetting and Uniform Interpolation in Extensions of the Description Logic EL , 2009, Description Logics.

[24]  Renate A. Schmidt,et al.  The Ackermann approach for modal logic, correspondence theory and second-order reduction , 2012, J. Appl. Log..

[25]  Valentin Goranko,et al.  Algorithmic correspondence and completeness in modal logic. I. The core algorithm SQEMA , 2006, Log. Methods Comput. Sci..

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

[27]  Carsten Lutz,et al.  An Automata-Theoretic Approach to Uniform Interpolation and Approximation in the Description Logic EL , 2012, KR.

[28]  Marco Hollenberg,et al.  Logical questions concerning the μ-calculus: Interpolation, Lyndon and Łoś-Tarski , 2000, Journal of Symbolic Logic.

[29]  R. Reiter,et al.  Forget It ! , 1994 .