Abstract
This paper proposes a modular method, called generalized product, of combining two coalgebraic hybrid logics in a parallel but non-compositional way. This is a coalgebraic generalization of a hybrid extension of product of modal logics. Our method, however, covers not only the combination of the same-type logics but also the combination of two different-type logics, e.g., graded hybrid logic and non-monotone hybrid logic. Moreover, we provide general strong completeness results for generalized products of coalgebraic hybrid logics with generic criteria.
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References
Schröder, L.: A finite model construction for coalgebraic modal logic. The Journal of Logic and Algebraic Programming 73, 97–110 (2007)
Schröder, L., Pattinson, D.: Rank-1 modal logics are coalgebraic. Journal of Logic and Computation 30(5), 1113–1147 (2008)
Myers, R., Pattinson, D., Schröder, L.: Coalgebraic hybrid logic. In: de Alfaro, L. (ed.) FOSSACS 2009. LNCS, vol. 5504, pp. 137–151. Springer, Heidelberg (2009)
Schröder, L., Pattinson, D.: Named models in coalgebraic hybrid logic. In: Marion, J.Y., Schwentick, T. (eds.) Proceedings of STACS 2010. Leibniz International Proceedings in Informatics, pp. 645–656 (2010)
Myers, R., Pattinson, D.: Hybrid logic with the difference modality for generalisations of graphs. Journal of Applied Logic 8(4), 441–458 (2010)
Schröder, L., Pattinson, D.: Modular algorithms for heterogeneous modal logics. In: Arge, L., Cachin, C., Jurdziński, T., Tarlecki, A. (eds.) ICALP 2007. LNCS, vol. 4596, pp. 459–471. Springer, Heidelberg (2007)
Schild, K.: Combining terminological logics with tense logic. In: Damas, L.M.M., Filgueiras, M. (eds.) EPIA 1993. LNCS, vol. 727, pp. 105–120. Springer, Heidelberg (1993)
Wolter, F., Zakharyaschev, M.: Modal description logics: modalizing roles. Fundamenta Informaticae 39, 411–438 (1999)
Kurucz, A.: Combining modal logcs. In: Blackburn, P., van Benthem, J., Wolter, F. (eds.) Handbook of Modal Logic, pp. 869–924. Elsevier, Amsterdam (2007)
Gabbay, D.M., Shehtman, V.B.: Products of modal logics, part 1. Logic Journal of IGPL 6(1), 73–146 (1998)
van Benthem, J., Bezhanishvili, G., ten Cate, B., Sarenac, D.: Multimodal logics of products of topologies. Studia Logica 84(3), 369–392 (2006)
Chellas, B.: Basic conditional logic. Journal of Philosophcal Logic 4(2), 133–153 (1975)
Kock, A.: Strong functors and monoidal monads. Archiv der Mathematik 23, 114–120 (1972)
Sano, K.: Axiomatizing hybrid products: How can we reason many-dimensionally in hybrid logic? Journal of Applied Logic 8(4), 459–474 (2010)
Sano, K.: Axiomatizing hybrid products of monotone neighbourhood frames. In: Accepted for the Publication in HyLo 2010 Post-Proceedings (2010), http://www.geocities.jp/k2sn/pro_hytop.pdf
Fine, K.: In so many possible worlds. Notre Dame Journal of Formal Logic 13(4), 516–520 (1972)
Blackburn, P., de Rijke, M., Venema, Y.: Modal Logic. Cambridge Tracts in Theoretical Computer Science. Cambridge University Press, Cambridge (2001)
Blackburn, P., ten Cate, B.: Pure extensions, proof rules, and hybrid axiomatics. Studia Logica 84(3), 277–322 (2006)
Schröder, L., Pattinson, D.: Strong completeness of coalgebraic modal logics. In: Albers, S., Marion, J.Y. (eds.) Proceedings of STACS 2009, vol. 3, pp. 673–684. Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik (2009)
ten Cate, B., Litak, T.: Topological perspective on the hybrid proof rules. Electronic Notes in Theoretical Computer Science 174(6), 79–94 (2007)
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Sano, K. (2011). Generalized Product of Coalgebraic Hybrid Logics. In: Corradini, A., Klin, B., Cîrstea, C. (eds) Algebra and Coalgebra in Computer Science. CALCO 2011. Lecture Notes in Computer Science, vol 6859. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22944-2_23
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DOI: https://doi.org/10.1007/978-3-642-22944-2_23
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