Abstract
We present ongoing work into the systematic study of the use of dual adjunctions in coalgebraic modal logic. We introduce a category of internal models for a modal logic. These are constructed from syntax, and yield a generalised notion of canonical model. Further, expressivity of a modal logic is shown to be characterised by factorisation of its models via internal models and the existence of cospans of internal models.
Keywords
- Coalgebra
- Modal Logic
- Dual Adjunction
- Expressivity
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References
Adámek, J., Herrlich, H., Strecker, G.E.: Abstract and Concrete Categories. Wiley, New York (1990)
Blackburn, P., de Rijke, M., Venema, Y.: Modal Logic. Cambridge University Press (2001)
Danos, V., Desharnais, J., Laviolette, F., Panangaden, P.: Bisimulation and cocongruence for probabilistic systems. Information and Computation 204(4), 503–523 (2006)
Doberkat, E.-E.: Stochastic Coalgebraic Logic. Springer, Heidelberg (2009)
Hasuo, I.: Generic Forward and Backward Simulations. In: Baier, C., Hermanns, H. (eds.) CONCUR 2006. LNCS, vol. 4137, pp. 406–420. Springer, Heidelberg (2006)
Jacobs, B., Sokolova, A.: Exemplaric Expressivity of Modal Logics. Journal of Logic and Computation 20(5), 1041–1068 (2010)
Kapulkin, K., Kurz, A., Velebil, J.: Expressivity of Coalgebraic Logic over Posets. CMCS 2010 Short contributions CWI Technical report SEN-1004:16–17 (2010)
Klin, B.: Coalgebraic modal logic beyond sets. Electronic Notes in Theoretical Computer Science 173, 177–201 (2007)
Kupke, C., Kurz, A., Pattinson, D.: Algebraic semantics for coalgebraic logics. Electronic Notes in Theoretical Computer Science 106, 219–241 (2004)
Kupke, C., Kurz, A., Venema, Y.: Stone coalgebras. Theoretical Computer Science 327(1-2), 109–134 (2004)
Kupke, C., Kurz, A., Pattinson, D.: Ultrafilter Extensions for Coalgebras. In: Fiadeiro, J.L., Harman, N.A., Roggenbach, M., Rutten, J. (eds.) CALCO 2005. LNCS, vol. 3629, pp. 263–277. Springer, Heidelberg (2005)
Pavlovic, D., Mislove, M., Worrell, J.B.: Testing Semantics: Connecting Processes and Process Logics. In: Johnson, M., Vene, V. (eds.) AMAST 2006. LNCS, vol. 4019, pp. 308–322. Springer, Heidelberg (2006)
Rutten, J.: Universal coalgebra: a theory of systems. Theoretical Computer Science 249(1), 3–80 (2000)
Schröder, L., Pattinson, D.: Strong completeness of coalgebraic modal logics. Leibniz International Proceedings in Informatics 3, 673–684 (2009)
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Wilkinson, T. (2012). Internal Models for Coalgebraic Modal Logics. In: Pattinson, D., Schröder, L. (eds) Coalgebraic Methods in Computer Science. CMCS 2012. Lecture Notes in Computer Science, vol 7399. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32784-1_13
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DOI: https://doi.org/10.1007/978-3-642-32784-1_13
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-32783-4
Online ISBN: 978-3-642-32784-1
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