Simulating Without Negation

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-fret 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.

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