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Journal of Logic and Computation 2001 11(5):701-715; doi:10.1093/logcom/11.5.701
© 2001 by Oxford University Press
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Modal Logic with Bounded Quantification over Worlds

Rogier M. Van Eijk1, Frank S. De Boer1, Wiebe Van Der Hoek1,2 and John-Jules Ch. Meyer1

1 Institute of Information and Computing Sciences, Utrecht University, P.O. Box 80.089, 3508 TB Utrecht, The Netherlands. E-mail: {rogier,frankb,wiebe,jj}@cs.uu.nl 2 Department of Philosophy, Utrecht University, The Netherlands and Department of Computer Science, University of Liverpool, UK

In this paper, we present a logical framework that combines modality with a first-order variable-binding mechanism. The logic, which belongs to the family of hybrid languages, differs from standard first-order modal logics in that quantification is not performed inside the worlds of a model, but the worlds in the model themselves constitute the domain of quantification. The locality principle of modal logic is preserved via the condition that in each world, the domain of quantification is given by a subset of the entire set of worlds in the model. In comparison with standard hybrid languages, the logic covers separate mechanisms for navigation and for variable-binding and formalizes reasoning about the worlds of a model in terms of equational logic. We show that the logic is semantically characterized by a generalization of classical bisimulation, called history-based bisimulation, and study the application of the logic to describe and reason about network topologies.

Keywords: Modal logics; equational logic; bounded quantification over worlds; history-; based bisimulation; network topologies; hybrid languages


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