Studia Logica 96 (1):65-93 (2010)

The variety of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\bf N4}^\perp}$$\end{document}-lattices provides an algebraic semantics for the logic \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\bf N4}^\perp}$$\end{document}, 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 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\bf N4}^\perp}$$\end{document}-lattices and their homomorphisms. The obtained duality naturally extends the Priestley duality for Nelson algebras constructed by R. Cignoli and A. Sendlewski.
Keywords Philosophy   Computational Linguistics   Mathematical Logic and Foundations   Logic
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DOI 10.1007/s11225-010-9274-2
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References found in this work BETA

Constructible Falsity.David Nelson - 1949 - Journal of Symbolic Logic 14 (1):16-26.
On the Representation of N4-Lattices.Sergei P. Odintsov - 2004 - Studia Logica 76 (3):385 - 405.
On Extensions of Intermediate Logics by Strong Negation.Marcus Kracht - 1998 - Journal of Philosophical Logic 27 (1):49-73.

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Citations of this work BETA

Priestley Duality for Bilattices.A. Jung & U. Rivieccio - 2012 - Studia Logica 100 (1-2):223-252.
Dualities for Modal N4-Lattices.R. Jansana & U. Rivieccio - 2014 - Logic Journal of the IGPL 22 (4):608-637.

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