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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.
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STABLE CANONICAL RULES

  • GURAM BEZHANISHVILI (a1), NICK BEZHANISHVILI (a2) and ROSALIE IEMHOFF (a3)
Abstract

We introduce stable canonical rules and prove that each normal modal multi-conclusion consequence relation is axiomatizable by stable canonical rules. We apply these results to construct finite refutation patterns for modal formulas, and prove that each normal modal logic is axiomatizable by stable canonical rules. We also define stable multi-conclusion consequence relations and stable logics and prove that these systems have the finite model property. We conclude the paper with a number of examples of stable and nonstable systems, and show how to axiomatize them.

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COPYRIGHT: © The Association for Symbolic Logic 2016 
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[1]Bezhanishvili, G. and Bezhanishvili, N., An algebraic approach to canonical formulas: Modal case. Studia Logica, vol. 99 (2011), no. 1–3, pp. 93–125.
[2]Bezhanishvili, G. and Bezhanishvili, N., Canonical formulas for wK4. Review of Symbolic Logic, vol. 5 (2012), no. 4, pp. 731–762.
[3]Bezhanishvili, G. and Bezhanishvili, N., Locally finite reducts of Heyting algebras and canonical formulas. Notre Dame Journal of Formal Logic, available as Utrecht University Logic Group Preprint Series Report 2013-3052015, to appear.
[4]Bezhanishvili, G., Bezhanishvili, N., and Ilin, J., Cofinal stable logics, 2015, available as ILLC Prepublication Series Report, PP-2015-08, submitted.
[5]Bezhanishvili, G., Bezhanishvili, N., and Ilin, J., Stable modal logics, 2015, in preparation.
[6]Bezhanishvili, G., Ghilardi, S., and Jibladze, M., An algebraic approach to subframe logics. Modal case. Notre Dame Journal of Formal Logic, vol. 52 (2011), no. 2, pp. 187–202.
[7]Bezhanishvili, G., Mines, R., and Morandi, P. J., Topo-canonical completions of closure algebras and Heyting algebras. Algebra Universalis, vol. 58 (2008), no. 1, pp. 1–34.
[8]Bezhanishvili, N., Lattices of Intermediate and Cylindric Modal Logics, PhD thesis, University of Amsterdam, Amsterdam, 2006.
[9]Bezhanishvili, N., Frame based formulas for intermediate logics. Studia Logica, vol. 90 (2008), no. 2, pp. 139–159.
[10]Bezhanishvili, N., Gabelaia, D., Ghilardi, S., and Jibladze, M, Admissible bases via stable canonical rules, 2015, available as ILLC Prepublication Series Report, PP-2015-14, submitted.
[11]Bezhanishvili, N. and Ghilardi, S., Multiple-conclusion rules, hypersequents syntax and step frames, Advances in Modal Logic (AiML 2014) (Gore, R., Kooi, B., and Kurucz, A., editors), College Publications, London, 2014, pp. 54–61. An extended version available as ILLC Prepublication Series Report PP-2014-05.
[12]Blackburn, P., de Rijke, M., and Venema, Y., Modal Logic, Cambridge University Press, Cambridge, 2001.
[13]Blok, W., On the degree of incompleteness of modal logics. Bulletin of Symbolic Logic, vol. 7 (1978), no. 4, pp. 167–175.
[14]Burris, R. and Sankappanavar, H., A Course in Universal Algebra, Springer, Berlin, 1981.
[15]Chagrov, A. and Zakharyaschev, M., Modal Logic, The Clarendon Press, New York, 1997.
[16]Conradie, W., Morton, W., and van Alten, C., An algebraic look at filtrations in modal logic. Logic Journal of IGPL, vol. 21 (2013), no. 5, pp. 788–811.
[17]Esakia, L., On the theory of modal and superintuitionistic systems, Logical Inference (Moscow, 1974), Nauka, Moscow, 1979, pp. 147–172 (in Russian).
[18]Ghilardi, S., Continuity, freeness, and filtrations. Journal of Applied Non-Classical Logics, vol. 20 (2010), no. 3, pp. 193–217.
[19]Goranko, V. and Passy, S., Using the universal modality: gains and questions. Journal of Logic and Computation, vol. 2 (1992), no. 1, pp. 5–30.
[20]Iemhoff, R., Consequence relations and admissible rules, to appear in the Journal of Philosophical Logic, available at http://dspace.library.uu.nl/handle/1874/282623, DOI: 10.1007/s10992-015-9380-8.
[21]Jeřábek, E., Canonical rules, this JOURNAL, vol. 74 (2009), no. 4, pp. 1171–1205.
[22]Kracht, M., Tools and Techniques in Modal Logic, North-Holland, Amsterdam, 1999.
[23]Kracht, M., Modal consequence relations, Handbook of Modal Logic (Blackburn, P., van Benthem, J., and Wolter, F., editors), pp. 491–545, Elsevier, Amsterdam, 2007.
[24]Lemmon, E. J., Algebraic semantics for modal logics. I, this Journal, vol. 31 (1966), pp. 46–65.
[25]Lemmon, E. J., Algebraic semantics for modal logics. II, this Journal, vol. 31 (1966), pp. 191–218.
[26]Lemmon, E. J., An Introduction to Modal Logic. The “Lemmon Notes” (Segerberg, Krister, editor), American Philosophical Quarterly Monograph Series, Vol. 11, Basil Blackwell, Oxford, 1977. In collaboration with Dana Scott.
[27]McKenzie, R., Equational bases and nonmodular lattice varieties. Transactions of the American Mathematical Society, vol. 174 (1972), pp. 1–43.
[28]McKinsey, J. C. C., A solution of the decision problem for the Lewis systems S2 and S4, with an application to topology, this Journal, vol. 6 (1941), pp. 117–134.
[29]McKinsey, J. C. C. and Tarski, A., The algebra of topology. Annals of Mathematics, vol. 45 (1944), pp. 141–191.
[30]Rautenberg, W., Splitting lattices of logics. Archive of Mathematical Logik, Grundlagen, vol. 20 (1980), no. 3–4, pp. 155–159.
[31]Rybakov, V. V., Admissibility of Logical Inference Rules, North-Holland, Amsterdam, 1997.
[32]Sambin, G., Subdirectly irreducible modal algebras and initial frames. Studia Logica, vol. 62 (1999), no. 2, pp. 269–282.
[33]Segerberg, K., An Essay in Classical Modal Logic. Vols. 1, 2, 3, Filosofiska Föreningen och Filosofiska Institutionen vid Uppsala Universitet, Uppsala, 1971.
[34]Shehtman, V., “Everywhere” and “here”. Journal of Applied Non-Classical Logics, vol. 9 (1999), no. 2–3, pp. 369–379.
[35]Venema, Y., A dual characterization of subdirectly irreducible BAOs. Studia Logica, vol. 77 (2004), no. 1, pp. 105–115.
[36]Venema, Y., Algebras and coalgebras, Handbook of Modal Logic (Blackburn, P., van Benthem, J., and Wolter, F., editors), Elsevier, Amsterdam, 2007, pp.331–426.
[37]Wronski, A., Intermediate logics and the disjunction property. Reports on Mathematical Logic, vol. 1 (1973), pp. 39–51.
[38]Zakharyaschev, M., Canonical formulas for K4. I. Basic results, this Journal, vol. 57 (1992), no. 4, pp. 1377–1402.
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