Cheap Boolean Role Constructors for Description Logics Technical Report

We investigate the possibility of incorporating Boolean role constructors on simple roles into some of today’s most popular description logics, f ocussing on cases where those extensions do not increase complexity of reas ning. We show that the expressive DLs SHOIQ andSROIQ, serving as the logical underpinning of OWL and the forthcoming OWL 2, can accommodate arbitr y Boolean expressions. The prominent OWL-fragment SHIQ can be safely extended by safe role expressions, and the tractable fragments EL and DLP retain tractability if extended by conjunction on roles, where in the case of DLP th e restriction on role simplicity can even be discarded.

[1]  Ian Horrocks,et al.  The Even More Irresistible SROIQ , 2006, KR.

[2]  Alex Borgiday.  On the Relative Expressiveness of Description Logics and Predicate Logics , 1996 .

[3]  Carsten Lutz,et al.  PDL with negation of atomic programs , 2004, J. Appl. Non Class. Logics.

[4]  Ulrike Sattler,et al.  The Complexity of Reasoning with Boolean Modal Logics , 2000, Advances in Modal Logic.

[5]  Sebastian Rudolph,et al.  Terminological Reasoning in SHIQ with Ordered Binary Decision Diagrams , 2008, AAAI.

[6]  Franz Baader,et al.  Pushing the EL Envelope , 2005, IJCAI.

[7]  Sebastian Rudolph,et al.  All Elephants are Bigger than All Mice , 2008, Description Logics.

[8]  Boris Motik,et al.  Reasoning in description logics using resolution and deductive databases , 2006 .

[9]  David Maier,et al.  The Theory of Relational Databases , 1983 .

[10]  Stéphane Demri,et al.  Deciding Regular Grammar Logics with Converse Through First-Order Logic , 2003, J. Log. Lang. Inf..

[11]  Sebastian Rudolph,et al.  Conjunctive Queries for a Tractable Fragment of OWL 1.1 , 2007, ISWC/ASWC.

[12]  Sebastian Rudolph,et al.  Expressive Tractable Description Logics based on SROIQ Rules , 2008 .

[13]  Diego Calvanese,et al.  Answering Regular Path Queries in Expressive Description Logics: An Automata-Theoretic Approach , 2007, AAAI.

[14]  Yevgeny Kazakov,et al.  SRIQ and SROIQ are Harder than SHOIQ , 2008, Description Logics.

[15]  Ian Pratt-Hartmann.  Complexity of the Two-Variable Fragment with Counting Quantifiers , 2005, J. Log. Lang. Inf..

[16]  Renate A. Schmidt,et al.  Using Tableau to Decide Expressive Description Logics with Role Negation , 2007, ISWC/ASWC.

[17]  Stephan Tobies,et al.  Complexity results and practical algorithms for logics in knowledge representation , 2001, ArXiv.

[18]  Ian Horrocks,et al.  Description logic programs: combining logic programs with description logic , 2003, WWW '03.

[19]  Sebastian Rudolph,et al.  Complexity Boundaries for Horn Description Logics , 2007, AAAI.

[20]  Diego Calvanese,et al.  The Description Logic Handbook: Theory, Implementation, and Applications , 2003, Description Logic Handbook.