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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.

Registro:

Documento: Artículo
Título:Residuated lattices as an algebraic semantics for paraconsistent nelson's logic
Autor:Busaniche, M.; Cignoli, R.
Filiación:Instituto de Matemática Aplicada Del Litoral- FIQ, CONICET-UNL, Guemes 3450, S3000GLN-Santa Fe, Argentina
Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Ciudad Universitaria, 1428 Buenos Aires, Argentina
Palabras clave:Constructive logic; N4-lattices; Paraconsistent Nelson's logic; Residuated lattices with involution; Twist-structures; Algebraic semantic; Constructive logic; matrix; Paraconsistent logic; Residuated lattices; Combinatorial circuits; Semantics; Formal logic
Año:2009
Volumen:19
Número:6
Página de inicio:1019
Página de fin:1029
DOI: http://dx.doi.org/10.1093/logcom/exp028
Título revista:Journal of Logic and Computation
Título revista abreviado:J Logic Comput
ISSN:0955792X
CODEN:JLCOE
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0955792X_v19_n6_p1019_Busaniche

Referencias:

  • Belnap, N.D., A useful four-valued logic (1977) Modern Uses of Multiple-Valued Logic, pp. 7-37. , G. Epstein and M. J. Dunn, eds. Reidel, Dordrecht
  • Blok, W.J., Pigozzi, D., Algebraic logic (1989) Memoirs of the American Mathematical Society, 77
  • Busaniche, M., Cignoli, R., Constructive logic with strong negation as a substructural logic (2008) Journal of Logic and Computation, , doi: 10.1093/logcom/exn081
  • Fidel, M.M., An algebraic study of a propositional system of Nelson (1978) Lectures in Pure and Applied Mathematics, 39, pp. 99-117. , Mathematical Logic. Proceedings of the First Brazilian Conference.A. I. Arruda, N. C. A. da Costa, R. Chuaqui, eds, Marcel Dekker, New York and Basel
  • Galatos, N., Jipsen, P., Kowalski, T., Ono, H., Residuated lattices: An algebraic glimpse at substructural logics (2007) Studies in Logics and TheFoundations of Mathematics, 151. , Elsevier, New York
  • Galatos, N., Raftery, J.G., Adding involution to residuated structures (2004) Stud. Log., 77, pp. 181-207
  • Hart, J.B., Rafter, L., Tsinakis, C., The structure of commutative residuated lattices (2002) Int. J. Algebra Comput., 12, pp. 509-524
  • Odintsov, S.P., Algebraic semantics for paraconsistent Nelson's logic (2003) Journal of Logic and Computation, 13, pp. 453-468
  • Odintsov, S.P., On the representation of N4-lattices (2004) Stud. Log., 76, pp. 385-405
  • Odintsov, S.P., On the class of extensions of nelsońs paraconsistent logic (2005) Stud. Log., 80, pp. 291-320
  • Sendlewski, A., Nelson algebras through Heyting ones. I (1990) Stud. Log., 49, pp. 105-126
  • Spinks, M., Veroff, R., Constructive logic with strong negation is a substructural logic. i (2008) Stud. Log., 88, pp. 325-348
  • Spinks, M., Veroff, R., Constructive logic with strong negation is a substructural logic. II (2008) Stud. Log., 89, pp. 401-425
  • Tsinakis, C., Wille, A.M., Minimal varieties of involutive residuated lattices (2006) Stud. Log., 83, pp. 407-423
  • Vakarelov, D., Notes on N-lattices and constructive logic with strong negation (1977) Stud. Log., 34, pp. 109-125

Citas:

---------- APA ----------
Busaniche, M. & Cignoli, R. (2009) . Residuated lattices as an algebraic semantics for paraconsistent nelson's logic. Journal of Logic and Computation, 19(6), 1019-1029.
http://dx.doi.org/10.1093/logcom/exp028
---------- CHICAGO ----------
Busaniche, M., Cignoli, R. "Residuated lattices as an algebraic semantics for paraconsistent nelson's logic" . Journal of Logic and Computation 19, no. 6 (2009) : 1019-1029.
http://dx.doi.org/10.1093/logcom/exp028
---------- MLA ----------
Busaniche, M., Cignoli, R. "Residuated lattices as an algebraic semantics for paraconsistent nelson's logic" . Journal of Logic and Computation, vol. 19, no. 6, 2009, pp. 1019-1029.
http://dx.doi.org/10.1093/logcom/exp028
---------- VANCOUVER ----------
Busaniche, M., Cignoli, R. Residuated lattices as an algebraic semantics for paraconsistent nelson's logic. J Logic Comput. 2009;19(6):1019-1029.
http://dx.doi.org/10.1093/logcom/exp028