Abstract
The variety of \({{\bf N4}^\perp}\)-lattices provides an algebraic semantics for the logic \({{\bf N4}^\perp}\) , a version of Nelson’s logic combining paraconsistent strong negation and explosive intuitionistic negation. In this paper we construct the Priestley duality for the category of \({{\bf N4}^\perp}\)-lattices and their homomorphisms. The obtained duality naturally extends the Priestley duality for Nelson algebras constructed by R. Cignoli and A. Sendlewski.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Cignoli R.: ‘The class of Kleene algebras satisfying interpolation preperty and Nelson algebras’. Algebra Universalis 23, 262–292 (1986)
Cornish W.H., Fowler P.R.: ‘Coproducts of De Morgan algebras’. Bull. Austral. Math. Soc. 16, 1–13 (1977)
Cornish W.H., Fowler P.R.: ‘Coproducts of Kleene algebras’. J. Austral. Math. Soc. (Ser. A) 27, 209–220 (1979)
Davey B.A., Priestley H.A.: Introduction to Lattices and Order. Cambridge University Press, Cambridge (2002)
Fidel, M.M., ‘An algebraic study of a propositional system of Nelson’, in Mathematical Logic, Proc. of the First Brasilian Conference, Campinas 1977, CRC Press, 1978, pp. 99–117.
Kracht M.: ‘On extensions of intermediate logics by strong negation’. Journal of Philosophical Logic 27, 49–73 (1998)
Monteiro A.: ‘Construction des algèbres de Nelson finies’. Bull. Acad. Pol. Sci. 11, 359–362 (1963)
Nelson D.: ‘Constructible falsity’. Journal of Symbolic Logic 14, 16–26 (1949)
Odintsov S.P.: ‘Algebraic semantics for paraconsistent Nelson’s logic’. Journal of Logic and Computation 13, 453–468 (2003)
Odintsov S.P.: ‘On representation of N4-lattices’. Studia Logica 76, 385–405 (2004)
Odintsov S.P.: ‘The class of extensions of Nelson paraconsistent logic’. Studia Logica 80, 291–320 (2005)
Odintsov S.P.: Constructive negations and paraconsistency. Springer, Dordrecht (2008)
Priestley H.A.: ‘Representation of distributive lattices by means of ordered Stone spaces’. Bull. London Math. Soc. 2, 186–190 (1970)
Priestley H.A.: ‘Order sets duality for distributive lattices’. Ann. Discrete Math. 23, 39–60 (1984)
Rasiowa, H., An algebraic approach to non-classical logics, North-Holland, Amsterdam, 1974.
Sendlewski, A., Equationally definable classes of Nelson algebras and their connection with classes of Heyting algebras, Institute of Mathematics of Nicholas Copernicus University, Torun’, 1984.
Sendlewski A.: ‘Topological duality for Nelson algebras and its application’. Bulletin of the Section of Logic, Polish Academy of Sciences 13, 257–280 (1984)
Sendlewski A.: ‘Nelson algebras through Heyting ones’. Studia Logica 49, 106–126 (1990)
Stone M.H.: ‘The theory of representations of Boolean algebras’. Trans. of Amer. Math. Society 40, 37–111 (1936)
Stone M.H.: ‘Topological representation of distributive lattices and Brouwerian algebras’. Casopis Pest. Math. 67, 1–25 (1937)
Vakarelov D.: ‘Notes on N-lattices and constructive logic with strong negation’. Studia Logica 36, 109–125 (1977)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Odintsov, S.P. Priestley Duality for Paraconsistent Nelson’s Logic. Stud Logica 96, 65–93 (2010). https://doi.org/10.1007/s11225-010-9274-2
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11225-010-9274-2