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Journal of Logic and Computation Advance Access published online on May 4, 2009
Journal of Logic and Computation, doi:10.1093/logcom/exp028
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© The Author, 2009. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

Original Papers

Residuated Lattices as an Algebraic Semantics for Paraconsistent Nelson's Logic

Manuela Busaniche

Instituto de Matemática Aplicada del Litoral- FIQ, CONICET-UNL, Guemes 3450, S3000GLN-Santa Fe, Argentina.
E-mail: manuelabusaniche{at}yahoo.com.ar

Roberto Cignoli

Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, 1428 Buenos Aires–Argentina.
E-mail: cignoli{at}dm.uba.ar

Received 22 January 2009.


  Abstract

The class of NPc-lattices is introduced as a quasivariety of commutative residuated lattices, and it is shown that the class of pairs (A,A+) such that A is an NPc-lattice and A+ is its positive cone, is a matrix semantics for Nelson paraconsistent logic.

Keywords: Paraconsistent Nelson's logic; N4-lattices; residuated lattices with involution; twist-structures; constructive logic


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