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The Impact of Including Model Update Operators in Modal Logics

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Part of the Lecture Notes in Computer Science book series (LNTCS,volume 8607)

Abstract

In this paper we discuss ideas about dynamic modal logics. Modal logics are appropriate to describe properties of relational structures, and several operators have been already introduced to describe dynamic properties of such structures. However, we are interested in those operators which can modify models during the evaluation of a formula. First, we introduce different dynamic operators to clarify which of them are interesting for us. Then we focus on operators which modify the accessibility relation of relational models, and we show some expressivity results.

Keywords

  • modal logics
  • model updates
  • bisimulation
  • complexity

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References

  1. Areces, C., Fervari, R., Hoffmann, G.: Moving arrows and four model checking results. In: Ong, L., de Queiroz, R. (eds.) WoLLIC 2012. LNCS, vol. 7456, pp. 142–153. Springer, Heidelberg (2012)

    CrossRef  Google Scholar 

  2. Areces, C., Fervari, R., Hoffmann, G.: Tableaux for relation-changing modal logics. In: Fontaine, P., Ringeissen, C., Schmidt, R.A. (eds.) FroCoS 2013. LNCS (LNAI), vol. 8152, pp. 263–278. Springer, Heidelberg (2013)

    CrossRef  Google Scholar 

  3. Areces, C., Fervari, R., Hoffmann, G.: Swap logic. Logic Journal of the IGPL 22(2), 309–332 (2014)

    CrossRef  MathSciNet  Google Scholar 

  4. Areces, C., Figueira, D., Figueira, S., Mera, S.: Expressive power and decidability for memory logics. In: Hodges, W., de Queiroz, R. (eds.) Logic, Language, Information and Computation. LNCS (LNAI), vol. 5110, pp. 56–68. Springer, Heidelberg (2008)

    CrossRef  Google Scholar 

  5. Areces, C., Figueira, D., Figueira, S., Mera, S.: The expressive power of memory logics. The Review of Symbolic Logic 4(2), 290–318 (2011)

    CrossRef  MATH  MathSciNet  Google Scholar 

  6. Areces, C., Figueira, D., Gorín, D., Mera, S.: Tableaux and model checking for memory logics. In: Giese, M., Waaler, A. (eds.) TABLEAUX 2009. LNCS (LNAI), vol. 5607, pp. 47–61. Springer, Heidelberg (2009)

    CrossRef  Google Scholar 

  7. Aucher, G., Balbiani, P., Fariñas Del Cerro, L., Herzig, A.: Global and local graph modifiers. Electronic Notes in Theoretical Computer Science (ENTCS), Special issue Proceedings of the 5th Workshop on Methods for Modalities (M4M5 2007) 231, 293–307 (2009)

    CrossRef  Google Scholar 

  8. Blackburn, P., de Rijke, M., Venema, Y.: Modal Logic. Cambridge Tracts in Theoretical Comp. Scie, vol. 53. Cambridge University Press (2001)

    Google Scholar 

  9. Blackburn, P., van Benthem, J.: Modal logic: A semantic perspective. In: Handbook of Modal Logic. Elsevier, North-Holland (2006)

    Google Scholar 

  10. Enderton, H.: A mathematical introduction to logic. Academic Press (1972)

    Google Scholar 

  11. Fervari, R.: Relation-Changing Modal Logics. PhD thesis, Facultad de Matemática Astronomía y Física, Universidad Nacional de Córdoba, Córdoba, Argentina (March 2014)

    Google Scholar 

  12. Fischer, M., Ladner, R.: Propositional dynamic logic of regular programs. J. Comput. Syst. Sci. 18(2), 194–211 (1979)

    CrossRef  MATH  MathSciNet  Google Scholar 

  13. French, T., van der Hoek, W., Iliev, P., Kooi, B.: On the succinctness of some modal logics. Artificial Intelligence 197, 56–85 (2013)

    CrossRef  MATH  MathSciNet  Google Scholar 

  14. Harel, D.: Dynamic logic. In: Gabbay, D., Guenthner, F. (eds.) Handbook of Philosophical Logic. Vol. II. Synthese Library, vol. 165, pp. 497–604. D. Reidel Publishing Co., Dordrecht (1984); Extensions of classical logic

    Google Scholar 

  15. Kooi, B., Renne, B.: Arrow update logic. Review of Symbolic Logic 4(4), 536–559 (2011)

    CrossRef  MATH  MathSciNet  Google Scholar 

  16. Ladner, R.: The computational complexity of provability in systems of modal propositional logic. SIAM J. Comput. 6(3), 467–480 (1977)

    CrossRef  MATH  MathSciNet  Google Scholar 

  17. Löding, C., Rohde, P.: Solving the sabotage game is PSPACE-hard. In: Rovan, B., Vojtáš, P. (eds.) MFCS 2003. LNCS, vol. 2747, pp. 531–540. Springer, Heidelberg (2003)

    CrossRef  Google Scholar 

  18. Lutz, C.: Complexity and succinctness of public announcement logic. In: Nakashima, H., Wellman, M.P., Weiss, G., Stone, P. (eds.) AAMAS, pp. 137–143. ACM (2006)

    Google Scholar 

  19. Mera, S.: Modal Memory Logics. PhD thesis, Univ. de Buenos Aires and UFR STMIA - Ecole Doctorale IAEM Lorraine Dép. de Form. Doct. en Informat. (2009)

    Google Scholar 

  20. Plaza, J.: Logics of public communications. Synthese 158(2), 165–179 (2007)

    CrossRef  MATH  MathSciNet  Google Scholar 

  21. Rohde, P.: On games and logics over dynamically changing structures. PhD thesis, RWTH Aachen (2006)

    Google Scholar 

  22. van Benthem, J.: An essay on sabotage and obstruction. In: Hutter, D., Stephan, W. (eds.) Mechanizing Mathematical Reasoning. LNCS (LNAI), vol. 2605, pp. 268–276. Springer, Heidelberg (2005)

    CrossRef  Google Scholar 

  23. van Ditmarsch, H., van der Hoek, W., Kooi, B.: Dynamic Epistemic Logic. Kluwer (2007)

    Google Scholar 

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Fervari, R. (2014). The Impact of Including Model Update Operators in Modal Logics. In: Colinet, M., Katrenko, S., Rendsvig, R.K. (eds) Pristine Perspectives on Logic, Language, and Computation. ESSLLI ESSLLI 2013 2012. Lecture Notes in Computer Science, vol 8607. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44116-9_7

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  • DOI: https://doi.org/10.1007/978-3-662-44116-9_7

  • Publisher Name: Springer, Berlin, Heidelberg

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