Priestley Duality for Paraconsistent Nelson’s Logic

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


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.



    Upload a copy of this work     Papers currently archived: 93,296

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

Hard Provability Logics.Mojtaba Mojtahedi - 2021 - In Mojtaba Mojtahedi, Shahid Rahman & MohammadSaleh Zarepour (eds.), Mathematics, Logic, and their Philosophies: Essays in Honour of Mohammad Ardeshir. Springer. pp. 253-312.
Two-cardinal diamond and games of uncountable length.Pierre Matet - 2015 - Archive for Mathematical Logic 54 (3-4):395-412.
Minimal elementary end extensions.James H. Schmerl - 2017 - Archive for Mathematical Logic 56 (5-6):541-553.


Added to PP

26 (#631,520)

6 months
8 (#415,230)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

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

Add more citations

References found in this work

Constructible falsity.David Nelson - 1949 - Journal of Symbolic Logic 14 (1):16-26.
Constructive Negations and Paraconsistency.Sergei Odintsov - 2008 - Dordrecht, Netherland: Springer.
On extensions of intermediate logics by strong negation.Marcus Kracht - 1998 - Journal of Philosophical Logic 27 (1):49-73.
On the representation of n4-lattices.Sergei P. Odintsov - 2004 - Studia Logica 76 (3):385 - 405.

View all 7 references / Add more references