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Journal of Applied Mathematics
Volume 2014, Article ID 702326, 15 pages
Research Article

Optimised ExpTime Tableaux for over Finite Residuated Lattices

College of Mechatronics Engineering and Automation, National University of Defense Technology, Changsha 410073, China

Received 25 June 2013; Accepted 16 December 2013; Published 7 April 2014

Academic Editor: Hector Pomares

Copyright © 2014 Jian Huang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This study proposes to adopt a novel tableau reasoning algorithm for the description logic with semantics based on a finite residuated De Morgan lattice. The syntax, semantics, and logical properties of this logic are given, and a sound, complete, and terminating tableaux algorithm for deciding fuzzy ABox consistency and concept satisfiability problem with respect to TBox is presented. Moreover, based on extended and/or completion-forest with a series of sound optimization technique for checking satisfiability with respect to a TBox in the logic, a new optimized ExpTime (complexity-optimal) tableau decision procedure is presented here. The experimental evaluation indicates that the optimization techniques we considered result in improved efficiency significantly.