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Topological Aspects of Branching-Time Semantics

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Abstract

The aim of this paper is to present a new perspective under which branching-time semantics can be viewed. The set of histories (maximal linearly ordered sets) in a tree structure can be endowed in a natural way with a topological structure. Properties of trees and of bundled trees can be expressed in topological terms. In particular, we can consider the new notion of topological validity for Ockhamist temporal formulae. It will be proved that this notion of validity is equivalent to validity with respect to bundled trees.

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References

  1. Van Benthem, J., ‘Content versus wrapping: an essay in semantic complexity’, in M. Marx, L. Pólos, and M. Masuch, (eds.), Arrow Logic and Multi-Modal Logic, Studies in Logic, Language and Information, CSLI Publications, Stanford, 1996, pp. 203–219.

    Google Scholar 

  2. Van Benthem, J., ‘Temporal patterns and modal structure’, Logic J. of the IGPL, 7(1):7–26, 1999. Special issue on Tempora Logic.

    Google Scholar 

  3. Burgess, J., ‘Logic and time’, J. of Symbolic Logic, 44:556–582, 1979.

    Google Scholar 

  4. Gabbay, D., I. Hodkinson, and M. Reynolds, Temporal Logic: Mathematical Foundation and Computational Aspects, volume I, Oxford University Press, Oxford, 1994.

    Google Scholar 

  5. Nyikos, P. J., ‘On some non-Archimedean spaces of Alexandroff and Urysohn’, Topology and its Applications, 91:1–23, 1999.

    Google Scholar 

  6. Prior, A., Past, Present and Future, Clarendon, Oxford, 1967.

    Google Scholar 

  7. Sabbadin, M., ‘Semantica topologica per logiche del tempo ramificato’, ‘Laurea’ dissertation, Facoltà di Scienze MM.FF.NN., Università di Padova, February 2002.

  8. Segerberg, K., An Essay in Classical Modal Logic, Filosofiska Studier 13, University of Uppsala, 1971.

  9. Thomason, R., ‘Combination of tense and modality’, in D. Gabbay and F. Guenthner, (eds.), The Handbook of Philosophical Logic, volume II, chapter 3, Reidel, Dordrecht, 1984, pp. 135–165.

    Google Scholar 

  10. Zanardo, A., ‘Branching-time logic with quantification over branches: the point of view of modal logic’, J. of Symbolic Logic, 61(1):1–39, 1996.

    Google Scholar 

  11. Zanardo, A., ‘First-order and second-order aspects of branching-time semantics’, to appear in the Proceedings of HPLMC-02, Second International Workshop oh the History and Philosophy of Logic, Mathematics and Computation (San Sebastian, Spain, 7–9 November, 2002), 2003.

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Authors and Affiliations

  1. Via Leonardo Da Vinci 11, 35133, Padova, Italy

    Michela Sabbadin

  2. Dipartimento di Matematica P. A., Via Belzoni 7, 35131, Padova, Italy

    Alberto Zanardo

Authors
  1. Michela Sabbadin
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  2. Alberto Zanardo
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Sabbadin, M., Zanardo, A. Topological Aspects of Branching-Time Semantics. Studia Logica 75, 271–286 (2003). https://doi.org/10.1023/B:STUD.0000009560.90259.de

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  • DOI: https://doi.org/10.1023/B:STUD.0000009560.90259.de

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