Banner Portal
REMARKS ON AN ALGEBRAIC SEMANTICS FOR PARACONSISTENT NELSON’S LOGIC
Vol. 34 No. 1 (2011), Artigos
Vol. 34 No. 1 (2011)

REMARKS ON AN ALGEBRAIC SEMANTICS FOR PARACONSISTENT NELSON’S LOGIC

Artigos
Published 2015-11-29
Manuela Busaniche
Instituto de Matemática Aplicada del Litoral CONICET - UNL.
Roberto Cignoli
Facultad de Ciencias Exactas y Naturales/Universidad de Buenos Aires
PDF (Português (Brasil))

Keywords

Nelson logic. Paraconsistency. Residuated Lattices. Substructural Logic. Twist Structures.

How to Cite

BUSANICHE, Manuela; CIGNOLI, Roberto. REMARKS ON AN ALGEBRAIC SEMANTICS FOR PARACONSISTENT NELSON’S LOGIC. Manuscrito: International Journal of Philosophy, Campinas, SP, v. 34, n. 1, p. 99–114, 2015. Disponível em: https://periodicos.sbu.unicamp.br/ojs/index.php/manuscrito/article/view/8642012. Acesso em: 21 jul. 2024.
ACM ACS APA ABNT Chicago Harvard IEEE MLA Turabian Vancouver

Download Citation

Endnote/Zotero/Mendeley (RIS) BibTeX

Abstract

In the paper Busaniche and Cignoli (2009) we presented a quasivariety of commutative residuated lattices, called NPc-lattices, that serves as an algebraic semantics for paraconsistent Nelson’s logic. In the present paper we show that NPc-lattices form a subvariety of the variety of commutative residuated lattices, we study congruences of NPc-lattices and some subvarieties of NPc-lattices.
PDF (Português (Brasil))

References

ALMUKDAD, A. and NELSON, D. “Constructible falsity and inexact predicates”, J. Symb. Logic 49, p. 231–233, 1984.

BURRIS, S. And SANKAPPANAVAR, H. P. A Course in Universal Algebra Graduate Texts in Mathematics, Vol. 78. SpringerVerlag, New York - Heidelberg - Berlin, 1981.

BUSANICHE, M. and CIGNOLI, R. “Constructive logic with strong negation as a substructural logic”, J. Log. Comput., 20, p. 761– 793, 2010.

BUSANICHE, M. and CIGNOLI, R. “Residuated lattices as an algebraic semantics for paraconsistent Nelson logic”, J. Log. Comput., 19, p. 1019–1029, 2009. GALATOS, N. and RAFTERY, J. G. “Adding involution to residuated structures”, Stud. Log., 77, p. 181-207, 2004.

GALATOS, N., JIPSEN, P., KOWALSKI, T. and ONO, H. Residuated Lattices: An Algebraic Glimpse at Substructural Logics, Studies in Logics and the Foundations of Mathematics, Volume 151, Elsevier, New York, 2007.

HART, J.B., RAFTER, L. and TSINAKIS, C. “The structure of commutative residuated lattices”, Int. J. Algebra Comput. 12, p. 509–524, 2002.

NELSON, D. “Constructible falsity”, J. Symb. Logic. 14, p.16–26, 1949.

ODINTSOV, S.P. “Algebraic semantics for paraconsistent Nelson’s logic”, J. Log. Comput. 13, p. 453–468, 2003.

ODINTSOV, S.P. “On the representation of N4-lattices”, Stud. Log. 76, p. 385– 405, 2004.

ODINTSOV, S.P. Negations and Paraconsistency, Trends in Logic–Studia Logica Library 26. Springer. Dordrecht, 2008.

SENDLEWSKI, A. “Nelson algebras through Heyting ones. I”, Stud. Log. 49, p. 105–126, 1990.

SPINKS, M. and VEROFF, R. “Constructive logic with strong negation is a substructural logic. I”, Stud. Log., 88, p. 325–348, 2008.

SPINKS, M. and VEROFF, R. “Constructive logic with strong negation is a substructural logic. II”, Stud. Log., 89, p. 401– 425, 2008.

TSINAKIS, C. and WILLE, A.M. “Minimal Varieties of Involutive Residuated Lattices”, Stud. Log., 83, p. 407– 423, 2006.

Downloads

Download data is not yet available.