Model checking hybrid logics

We investigate the complexity of the model checking problem for hybrid logics. We provide model checker algorithms for various hybrid fragments and we prove PSPACE-completeness for hybrid fragments including binders. We complement and motivate our complexity results with an application of model checking in hybrid logic to the problems of query and constraint evaluation for semistructured data.

[1]  Jennifer Widom,et al.  The Lorel query language for semistructured data , 1997, International Journal on Digital Libraries.

[2]  Serge Abiteboul,et al.  Regular Path Queries with Constraints , 1999, J. Comput. Syst. Sci..

[3]  Stephan Merz,et al.  Model Checking , 2000 .

[4]  Luca de Alfaro,et al.  Model Checking the World Wide Web , 2001, CAV.

[5]  Wenfei Fan,et al.  Integrity constraints for XML , 2003, J. Comput. Syst. Sci..

[6]  Maarten de Rijke,et al.  A Modal Perspective on Path Constraints , 2003, J. Log. Comput..

[7]  E. Allen Emerson,et al.  Temporal and Modal Logic , 1991, Handbook of Theoretical Computer Science, Volume B: Formal Models and Sematics.

[8]  Dan Suciu,et al.  Containment and equivalence for an XPath fragment , 2002, PODS.

[9]  Wenfei Fan,et al.  Path constraints on semistructured and structured data , 1998, PODS '98.

[10]  Rance Cleaveland,et al.  A linear-time model-checking algorithm for the alternation-free modal mu-calculus , 1993, Formal Methods Syst. Des..

[11]  Serge Abiteboul,et al.  Foundations of Databases , 1994 .

[12]  Neil Immerman,et al.  On the Unusual Effectiveness of Logic in Computer Science , 2001, Bulletin of Symbolic Logic.

[13]  Roy Goldman,et al.  Lore: a database management system for semistructured data , 1997, SGMD.

[14]  M. de Rijke,et al.  CTL model checking for processing simple XPath queries , 2004, Proceedings. 11th International Symposium on Temporal Representation and Reasoning, 2004. TIME 2004..

[15]  Georg Gottlob,et al.  Monadic queries over tree-structured data , 2002, Proceedings 17th Annual IEEE Symposium on Logic in Computer Science.

[16]  M. de Rijke,et al.  Hybrid logics on linear structures: expressivity and complexity , 2003, 10th International Symposium on Temporal Representation and Reasoning, 2003 and Fourth International Conference on Temporal Logic. Proceedings..

[17]  Carlos Areces,et al.  HyLoRes 1.0: Direct Resolution for Hybrid Logics , 2002, CADE.

[18]  Valentin Goranko,et al.  Hierarchies of modal and temporal logics with reference pointers , 1996, J. Log. Lang. Inf..

[19]  Maarten de Rijke,et al.  Describing and Quering Semistructured Data: Some Expressiveness Results , 1998, BNCOD.

[20]  Maarten Marx,et al.  Hybrid logics: characterization, interpolation and complexity , 2001, Journal of Symbolic Logic.

[21]  Maarten Marx,et al.  Conditional XPath, the first order complete XPath dialect , 2004, PODS.

[22]  Elisa Quintarelli,et al.  Model-Checking Based Data Retrieval , 2004, Lecture Notes in Computer Science.

[23]  Dan Suciu,et al.  Data on the Web: From Relations to Semistructured Data and XML , 1999 .

[24]  Patrick Blackburn,et al.  Hybrid languages , 1995, J. Log. Lang. Inf..

[25]  Maarten Marx,et al.  The Computational Complexity of Hybrid Temporal Logics , 2000, Log. J. IGPL.

[26]  Tinko Tinchev,et al.  An Essay in Combinatory Dynamic Logic , 1991, Inf. Comput..

[27]  Jerzy Tiuryn,et al.  Dynamic logic , 2001, SIGA.

[28]  B. T. Cate,et al.  Model theory for extended modal languages , 2005 .

[29]  J W Ballard,et al.  Data on the web? , 1995, Science.

[30]  Diego Calvanese,et al.  Representing and Reasoning on XML Documents: A Description Logic Approach , 1999, J. Log. Comput..

[31]  M. de Rijke,et al.  Modal Logic , 2001, Cambridge Tracts in Theoretical Computer Science.

[32]  Maarten Marx,et al.  A Road-Map on Complexity for Hybrid Logics , 1999, CSL.