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Journal of Logic and Computation 1997 7(4):501-522; doi:10.1093/logcom/7.4.501
© 1997 by Oxford University Press
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Original Articles

Simulating without Negation

NATASHA KURTONINA and MAARTEN DE RIJKE

Center for Logic, Ghent University Rozier 44, 9000 Ghent, Belgium E-mail: natasha.kurtonina{at}rug.ac.be
Dept. of Computer Science, University of Warwick Coventry CV4 7AL, England E-mail: mdr{at}dcs.warwick.ac.uk

Although negation-free languages are widely used in logic and computer science, relatively little is known about their expressive power. To address this issue we consider kinds of non-symmetric bisimulations called directed simulations, and use these to analyse the expressive power and model theory of negation-free modal and temporal languages. We first use them to obtain preservation, safety and definability results for a simple negation-free modal language. We then obtain analogous results for stronger negation-free languages. Finally, we extend our methods to deal with languages with non-Boolean negation.

Keywords: Expressive power; modal logic; negation-free languages


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