Geodesic
On Belnapian modal algebras: representations, homomorphisms, congruences, and so on
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 10 (2013), pp. 517-534.

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We obtain a bunch of principal results on Belnapian modal algebras (henceforth called BK-lattices) — these results may serve as a semantical basis for further investigation of the lattice of extensions of Belnapian modal logic (denoted by BK here).
Keywords: many-valued modal logic, strong negation, twist-structure
Mots-clés : Belnapian modal logic, Belnapian modal algebra, modal algebra. 
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S. O. Speranski. On Belnapian modal algebras: representations, homomorphisms, congruences, and so on. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 10 (2013), pp. 517-534. http://geodesic.mathdoc.fr/item/SEMR_2013_10_a14/

[1] A. Almukdad, D. Nelson, “Constructible falsity and inexact predicates”, Journal of Symbolic Logic, 49 (1984), 231–233 | DOI | MR | Zbl

[2] S. N. Burris, H. P. Sankappanavar, A Course in Universal Algebra, The Millenium Edition, , 2000 http://math.uwaterloo.ca/s̃nburris/htdocs/UALG/univ-algebra.pdf

[3] N. D. Belnap, “How a computer should think”: G. Ryle, Contemporary Aspects of Philosophy, Oriel Press Ltd, Stockfield, 1977, 30–55

[4] W. J. Blok, D. Pigozzi, Algebraizable logics, Memoirs of the American Mathematical Society, 396, American Mathematical Society, Providence, 1989 | MR | Zbl

[5] R. Cignoli, “The class of Kleene algebras satisfying interpolation property and Nelson algebras”, Algebra Universalis, 23:3 (1986), 262–292 | DOI | MR | Zbl

[6] J. M. Dunn, “Intuitive semantics for first-degree entailments and coupled trees”, Philosophical Studies, 29 (1976), 149–168 | DOI | MR

[7] M. M. Fidel, “An algebraic study of a propositional system of Nelson”, Mathematical Logic, Proceedings of the First Brasilian Conference (Campinas, 1977), CRC Press, 1978, 99–117 | MR

[8] K. Gödel, “Eine interpretation des intuitionistischen aussagenkalküls”, Ergebnisse eines mathematischen Kolloquiums, 4 (1933), 39–40

[9] M. Kracht, Tools and Techniques in Modal Logic, Elseiver, Amsterdam, 1999 | MR | Zbl

[10] J. C. C. McKinsey, A. Tarski, “Some theorems about the sentential calculi of Lewis and Heyting”, Journal of Symboloc Logic, 13 (1948), 1–15 | DOI | MR | Zbl

[11] D. Nelson, “Constructible falsity”, Journal of Symbolic Logic, 14 (1949), 16–26 | DOI | MR | Zbl

[12] S. P. Odintsov, “Algebraic semantics for paraconsistent Nelson's logic”, Journal of Logic and Computation, 13 (2003), 453–468 | DOI | MR | Zbl

[13] S. P. Odintsov, “On the representation of $\mathbf{N4}$-Lattices”, Studia Logica, 76:3 (2004), 385–405 | DOI | MR | Zbl

[14] S. P. Odintsov, “The class of extensions of Nelson paraconsistent logic”, Studia Logica, 80:2–3 (2005), 291–320 | DOI | MR | Zbl

[15] S. P. Odintsov, Constructive Negations and Paraconsistency, Springer, Dordrecht, 2008 | MR | Zbl

[16] S. P. Odintsov, E. I. Latkin, “$\mathbf{BK}$-lattices. Algebraic semantics for Belnapian modal logics”, Studia Logica, 100:1–2 (2012), 319–338 | DOI | MR | Zbl

[17] S. P. Odintsov, H. Wansing, “Constructive predicate logic and constructive modal logic. Formal duality versus semantical duality”, First-order Logic Revised, eds. V. Hendricks et al., Logos Verlag, Berlin, 2004, 269–286 | Zbl

[18] S. P. Odintsov, H. Wansing, “Modal logic with Belnapian truth values”, Journal of Applied Non-classical Logics, 20 (2010), 270–301 | MR

[19] H. Rasiowa, “$N$-lattices and constructive logic with strong negation”, Fundamenta Mathematicae, 46 (1958), 61–80 | MR | Zbl

[20] H. Rasiowa, An Algebraic Approach to Non-classical Logics, North-Holland, Amsterdam, 1974 | MR | Zbl

[21] U. Rivieccio, “Paraconsistent modal logics”, Electronic Notes in Theoretical Computer Science, 278 (2011), 173–186 | DOI | MR

[22] A. Sendlewski, “Some investigations of varieties of $N$-lattices”, Studia Logics, 43:1 (1984), 257–280 | DOI | MR | Zbl

[23] A. Sendlewski, “Nelson algebras through Heyting ones, I”, Studia Logica, 49:1 (1990), 106–126 | DOI | MR

[24] E. Sherkhonov, “Modal operators over constructive logic”, Journal of Logic and Computation, 18 (2008), 815–829 | DOI | MR | Zbl

[25] S. O. Speranski, “On connections between $\mathbf{BK}$-extensions and $\mathbf{K}$-extensions”, Advances in Modal Logic, Short Presentations (Copenhagen, Denmark, 22–25 August 2012), ed. T. Bolander et al., 86–90

[26] S. O. Speranski, “On connections between $\mathbf{BK}$-extensions and $\mathbf{K}$-extensions”, Maltsev Meeting at Novosibirsk, Russia, 12–16 November 2012, Collection of Abstracts, 168

[27] D. Vakarelov, “Notes on $N$-lattices and constructive logic with strong negation”, Studia Logica, 36:1–2 (1977), 109–125 | DOI | MR | Zbl

[28] N. Vorob'ev, “A constructive propositional logic with strong negation”, Doklady Akademii Nauk SSSR, 85 (1952), 465–468 (in russian) | MR

[29] H. Wansing, “Connexive modal logic”, Advances in Modal Logic, King's College Publications, 5, eds. R. Schmidt et al., London, 2005, 367–383 | MR | Zbl

[30] H. Wansing, “Connexive logic”, Stanford Encyclopedia of Philosophy, ed. E. Zalta, 2006 http://plato.stanford.edu/entries/logic-connexive/