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Properties of Saturation in Monotonic Neighbourhood Models and Some Applications

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Abstract

In this paper we shall discuss properties of saturation in monotonic neighbourhood models and study some applications, like a characterization of compact and modally saturated monotonic models and a characterization of the maximal Hennessy-Milner classes. We shall also show that our notion of modal saturation for monotonic models naturally extends the notion of modal saturation for Kripke models.

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References

  1. Areces, C., and D. Figueira, Which semantics for neighbourhood semantics?, IJCAI’09, AAAI Press, Menlo Park, 2009, pp. 671–676.

  2. Blackburn, P., M. de Rijke, and Y. Venema, Modal Logic. Cambridge Tracts in Theoretical Computer Science. Cambridge University Press, 2001.

  3. Celani S. A.: Saturated neighbourhood models of monotonic modal logics. Revista de la Unión Matemática Argentina 49(1), 111–121 (2008)

    Google Scholar 

  4. Celani S.A.: Monotonic modal logics related to the Von Wright’s logic of place. Rend. Sem. Mat. Univ. Pol. Torino 66(1), 59–74 (2008)

    Google Scholar 

  5. Celani S.A.: Topological duality for Boolean algebras with a normal n-ary monotonic operator. Order 26(1), 49–67 (2009)

    Article  Google Scholar 

  6. Chellas B.F.: Modal Logic: An Introduction. Cambridge University Press, Cambridge (1980)

    Book  Google Scholar 

  7. Goldblatt, R., Mathematics of Modality, CSLI Lectures Notes 43, CSLI Publications, Stanford, 1993.

  8. Goldblatt, R., Saturation and the Hennessy-Milner property, in Alban Ponse, Maarten de Rijke, and Yde Venema (eds.), Modal Logic and Process Algebra, CSLI Lecture Notes No. 53, CSLI Publications, Stanford, 1995, pp. 107–129.

  9. Goldblatt R.: Axiomatic classes of intuitionistic models. Journal of Universal Computer Science 11(12), 1945–1962 (2005)

    Google Scholar 

  10. Hansen, H. H., Monotonic modal logic, Master’s Thesis, Preprint 2003-2024, ILLC, University of Amsterdam, 2003.

  11. Hansen, H. H., and C. Kupke, A Coalgebraic Perspective on Monotone Modal Logic, Electronic Notes in Theoretical Computer Science, vol. 106, Elsevier, Amsterdam, pp. 121–143, 2004.

  12. HansenH.H. Kupke C., Pacuit E.: Neighbourhood structures: bisimilarity and basic model theory. Logical Methods in Computer Science 5(2), 1–38 (2009)

    Google Scholar 

  13. Hollenberg, M. J., Hennessey-Milner classes and process algebra, in A. Ponse, M. de Rijke, and Y. Venema (eds.), Modal Logic and Process Algebra: A Bisimulation Perspective, vol. 53 of CSLI Lecture Notes. CSLI Publications, Stanford, 1995, pp. 187–216.

  14. Jaspars, J., Fused modal logic and inconsistent belief, in M. de Glas and D. M. Gabbay (eds.), Proceedings of the First World Conference on the Fundamentals of AI, Angkor Publishing Company, Paris, 1991, pp. 267–275.

  15. Jaspars, J., Logical omniscience and inconsistent belief, in M.de Rijke (ed.), Diamonds and Defaults, Kluwer, Dordrecht, 1993, pp. 129–146.

  16. Michael E.: Topologies on spaces of subsets. Transactions of American Mathematical Society 71, 152–182 (1951)

    Article  Google Scholar 

  17. Naumov P.: On modal logic of deductive closure. Annals of Pure and Applied Logic 141(1–2), 218–224 (2006)

    Article  Google Scholar 

  18. Segerberg, K., An Essay in Classical Modal Logic, Number 13 in Filosofiska Studier, Uppsala Universitet, Uppsala, 1971.

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Correspondence to Sergio A. Celani.

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Presented by Heinrich Wansing

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Celani, S.A. Properties of Saturation in Monotonic Neighbourhood Models and Some Applications. Stud Logica 103, 733–755 (2015). https://doi.org/10.1007/s11225-014-9590-z

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