Abstract
This work introduces modal logics for varieties of normal topological quasi-Boolean algebras. Relational semantics for these modal logics using involutive frames are established. A discrete duality is given for involutive frames and normal topological quasi-Boolean algebras. Some results on Kripke-completeness and finite model property are given.
This work was supported by Chinese National Funding of Social Sciences (Grant no. 18ZDA033).
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References
Banerjee, M., Chakraborty, M.K.: Rough sets through algebraic logic. Fundamenta Informatica 28(3–4), 211–221 (1996)
Belnap, N.: A useful four-valued logic. In: Dunn, J.M., Epstein, G. (eds.) Modern Uses of Multiple-Valued Logic, pp. 5–37. D. Reidel Publishing Company, Dordrecht (1977)
Blackburn, P., de Rijke, M., Venema, Y.: Modal Logic. Cambridge University Press, Cambridge (2001)
Blok, W.J.: Varieties of interior algebras. Ph.D. dissertation. University of Amsterdam (1976)
Białynicki-Birula, A., Rasiowa, H.: On the representation of quasi-Boolean algebras. Bulletin de l’Académie Polonaise des Sciences, Classe III, Bd. 5, 259–261 (1957)
Celani, S.: Classical modal De Morgan algebras. Stud. Logica 98, 251–266 (2011)
Celani, S.A., Jansana, R.: Priestley duality, a Sahlqvist theorem and a Goldblatt-Thomason theorem for positive modal logic. Log. J. IGPL 7(6), 683–715 (1999)
Celani, S.A.: Notes on the representation of distributive modal algebras. Miskolc Math. Notes 9(2), 81–89 (2008)
Chagrov, A., Zakharyaschev, M.: Modal Logic. Clarendon Press, Oxford (1997)
Davey, B.A., Priestley, H.A.: Introduction to Lattices and Order, 2nd edn. Cambridge University Press, Cambridge (2002)
Dunn, J.M.: The algebra of intensional logics. Ph.D. thesis. University of Pittsburg (1966)
Dunn, M.: Positive modal logic. Stud. Logica 55, 301–317 (1995)
Font, J.M., Rius, M.: An abstract algebraic logic approach to tetravalent modal logics. J. Symbolic Log. 65, 481–518 (2000)
Font, J.M.: Belnap’s four-valued logic and De Morgan lattices. Log. J. IGPL 5(3), 413–440 (1997)
Lin, Y., Ma, M.: Belnap-Dunn modal logic with value operators. Stud. Logica 109, 759–789 (2021)
Lin, Z., Ma, M.: Residuated algebraic structures in the vicinity of pre-rough algebras and decidability. Fundamenta Informatica 179, 239–174 (2021)
Loureiro, I.: Prime spectrum of a tetravalent modal algebra. Notre Dame J. Formal Log. 24, 389–394 (1983)
Odintsov, S.P., Speranski, S.O.: Belnap-Dunn modal logics: truth constants vs. truth values. Rev. Symbolic Log. 13(2), 416–435 (2020)
Odintsov, S.P., Wansing, H.: Modal logics with Belnapian truth values. J. Appl. Non-Classical Log. 20(3), 279–301 (2010)
Rasiowa, H.: An Algebraic Approach to Non-Classical Logics. North-Holland Publishing Company, Amsterdam (1974)
Saha, A., Sen, J., Chakraborty, M.K.: Algebraic structures in the vicinity of pre-rough algebra and their logics. Inf. Sci. 282, 296–320 (2014)
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Wu, H., Ma, M. (2023). Relational Semantics for Normal Topological Quasi-Boolean Logic. In: Banerjee, M., Sreejith, A.V. (eds) Logic and Its Applications. ICLA 2023. Lecture Notes in Computer Science, vol 13963. Springer, Cham. https://doi.org/10.1007/978-3-031-26689-8_15
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