Decision Procedures for Expressive Description Logics with Intersection, Composition, Converse of Roles and Role Identity

In the quest for expressive description logics for real-world applications, a powerful combination of constructs has so far eluded practical decision procedures: intersection and composition of roles. We propose tableau-based decision procedures for the satisfiability of logics extending ALC with the intersectionu, composition◦, uniont, converse ·− of roles and role identity id(·). We show that 1. the satisfiability of ALC(u,◦,t), for which a 2-EXPTIME upper bound was given by treeautomata techniques, is PSPACE-complete; 2. the satisfiability of ALC(u,◦,t, ·−, id(·)), an open problem so far, is in NEXPTIME.

[1]  Pierre Wolper,et al.  Automata theoretic techniques for modal logics of programs: (Extended abstract) , 1984, STOC '84.

[2]  Giuseppe De Giacomo,et al.  Combining Deduction and Model Checking into Tableaux and Algorithms for Converse-PDL , 2000, Inf. Comput..

[3]  Diego Calvanese,et al.  Dwq : Esprit Long Term Research Project, No 22469 on the Decidability of Query Containment under Constraints on the Decidability of Query Containment under Constraints , 2022 .

[4]  Stephan Tobies.  PSPACE Reasoning for Graded Modal Logics , 2001, J. Log. Comput..

[5]  Gert Smolka,et al.  Attributive Concept Descriptions with Complements , 1991, Artif. Intell..

[6]  Francesco M. Donini,et al.  Decidable reasoning in terminological knowledge representation systems , 1993 .

[7]  Harald Ganzinger,et al.  A superposition decision procedure for the guarded fragment with equality , 1999, Proceedings. 14th Symposium on Logic in Computer Science (Cat. No. PR00158).

[8]  Richard E. Ladner,et al.  The Computational Complexity of Provability in Systems of Modal Propositional Logic , 1977, SIAM J. Comput..

[9]  Fabio Massacci,et al.  Tableau Methods for Formal Verification of Multi-Agent Distributed Systems , 1998, J. Log. Comput..

[10]  Martin Otto,et al.  On Logics with Two Variables , 1999, Theor. Comput. Sci..

[11]  Alexander Borgida,et al.  On the Relative Expressiveness of Description Logics and Predicate Logics , 1996, Artif. Intell..

[12]  Franz Baader,et al.  Expressive Number Restrictions in Description Logics , 1999, J. Log. Comput..

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

[14]  Ian Horrocks,et al.  Reasoning with Axioms: Theory and Practice , 2000, KR.

[15]  Dimiter Vakarelov,et al.  Iteration-free PDL with Intersection: a Complete Axiomatization , 2001, Fundam. Informaticae.

[16]  Ian Horrocks,et al.  A Description Logic with Transitive and Inverse Roles and Role Hierarchies , 1999, J. Log. Comput..

[17]  Ian Horrocks,et al.  Practical Reasoning for Very Expressive Description Logics , 2000, Log. J. IGPL.

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

[19]  Luis Fariñas del Cerro,et al.  Modal Tableaux with Propagation Rules and Structural Rules , 1997, Fundam. Informaticae.

[20]  Klaus Schild,et al.  A Correspondence Theory for Terminological Logics: Preliminary Report , 1991, IJCAI.

[21]  Maurizio Lenzerini,et al.  What's in an Aggregate: Foundations for Description Logics with Tuples and Sets , 1995, IJCAI.

[22]  Alon Y. Levy.  Review - Decidable Reasoning in Terminological Knowledge Representation Systems. , 1999, SIGMOD 1999.

[23]  Ryszard Danecki,et al.  Nondeterministic Propositional Dynamic Logic with intersection is decidable , 1984, Symposium on Computation Theory.

[24]  Ian Horrocks,et al.  Practical Reasoning for Expressive Description Logics , 1999, LPAR.