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Journal of Logic and Computation, Volume 11, Issue 5, pp. 717-736: Abstract.

Resolution in Modal, Description and Hybrid Logic

Carlos Areces1, Maarten de Rijke1, and Hans de Nivelle2

1ILLC, University of Amsterdam, Nieuwe Achtergracht 166, 1018 WV Amsterdam, The Netherlands. E-mail: {carlos,mdr}@science.uva.nl
2Max Planck Institut für Informatik, Stuhlsatzenhausweg 85, 66123 Saarbrücken, Germany. E-mail: nivelle@mpi-sb.mpg.de

We provide a resolution-based proof procedure for modal, description and hybrid logic that improves on previous proposals in important ways. It avoids translations into large undecidable logics, and works directly on modal, description or hybrid logic formulas instead. In addition, by using the hybrid machinery it avoids the complexities of earlier propositional resolution-based methods for modal logic. It combines ideas from the method of prefixes used in tableaux, and resolution ideas in such a way that some of the heuristics and optimizations devised in either field are applicable.

Keywords: Direct resolution, modal logic, description logic, hybrid logic

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