Publicado

2018-07-01

Discriminant Structures Associated to Matrix Semantics

Estructuras Discriminantes Asociadas a Semánticas Matriciales

DOI:

https://doi.org/10.15446/recolma.v52n2.77158

Palabras clave:

Matrix Logic, n-valued logics, Discriminant Structures (en)
Lógica Matricial, lógicas n-valuadas, Estructuras Discriminantes (es)

Autores/as

  • Víctor Fernández Universidad Nacional de San Juan
  • Carina Murciano Universidad Nacional de San Juan
In this paper we show a method to characterize logical matrices by means of a special kind of structures, called here discriminant structures for this purpose. Its definition is based on the discrimination of each truthvalue of a given (finite) matrix M = (A, D), w.r.t. its belonging to D. From this starting point, we define a whole class SM of discriminant structures. This class is characterized by a set of Boolean equations, as it is shown here. In addition, several technical results are presented, and it is emphasized the relation of the Discriminant Structures Semantics (D.S.S) with other related semantics such as Dyadic or Twist-Structure.
En este artículo mostramos un método para caracterizar matrices lógicas por medio de una clase especial de estructuras, llamadas aquí estructuras discriminantes. Su definición es basada en la discriminación de cada valor de verdad de una matriz (finita) M = (A, D) dada, con respecto a su pertenencia a D. Con este punto de partida, definimos toda una clase SM de estructuras discriminantes. Esta clase es caracterizada por un conjunto de ecuaciones Booleanas, según aquí se indica. Además, son demostrados diversos resultados técnicos y se enfatiza la relación de la Semántica de Estructuras Discriminantes (D.S.S) con otras semánticas relacionadas tales como las Semánticas Diádicas o las Semánticas de Estructuras Twist.

Referencias

Carlos Caleiro, Walter Carnielli, Marcelo Coniglio, and Joao Marcos, Two's company: “The humbug of many logical values”, In Logica Universalis (J. Y. Beziáu ed.), 169 - 189, Birkhauser, Germany, 2005.

Carlos Caleiro, Joao Marcos, and Marco Volpe, Bivalent semantics, generalized compositionaly and analytic classic-like tableaux for finite-valued logics, Theoretical Computer Science 603 (2015), 84–110.

Janusz Czelakowski, Protoalgebraic logics, Kluwer Academic Publishers, Dordrecht, 2001.

Víctor Fernández, Society semantics for n-valued logics (in portuguese), Master's thesis, UNICAMP, Campinas, Brazil, june 2001.

Víctor Fernández and Carina Murciano, A Generalization of Twist-Structures Semantics for n-valued logics, CLE e-prints 13 (1), 2013 (available at http://logica.cle.unicamp.br/pub/e-prints/vol.13,n.1,2013.pdf).

Manuel Fidel, An Algebraic Study of a Propositional System of Nelson, Proceedings of the First Brazilian Conference on Mathematical Logic (Campinas, 1977), 99–117, 1978, 1978.

Sergei Odintsov, Algebraic Semantics for Paraconsistent Nelson's logic, Journal of Logic and Computation 13 (2003), 453–468.

Fernando Ramos and Víctor Fernández, Twist - Structures Semantics for the Logics of the Hierarchy InPk, Journal of Applied Non-Classical Logics 19 (2009), 183–209.

Umberto Rivieccio, Implicative Twist-Structures, Algebra Universalis 71 (2014), 155–186.

Antonio Sette, On the Propositional Calculus P1, Mathematica Japonicae 18 (1973), 173–180.

Antonio Sette and Walter Carnielli, Maximal weakly-intuitionistic logics, Studia Logica 55 (1995), 181–203.

Timothy Smiley, The Independence of Connectives, The Journal of Symbolic Logic 27 (1962), 426–436.

Roman Suszko, The Fregean axiom and Polish Mathematical Logic in the 1920’s, Studia Logica 36 (1977), 373–380.

Alasdair Urquhart, A Finite Matrix whose consequence relation is not finitely axiomatizable, Reports on Mathematical Logic 9 (1977), 71–73.

Dimiter Vakarelov, Notes on N-lattices and Constructive Logic with Strong Negation, Studia Logica 36 (1977), 109–125.

Ryszard Wójcicki, Referential Matrix Semantics for Propositional Calculi, Bulletin of the Section of Logic 8 (1979), 170–176.

Cómo citar

APA

Fernández, V., & Murciano, C. (2018). Discriminant Structures Associated to Matrix Semantics. Revista Colombiana de Matemáticas, 52(2), 185-209. https://doi.org/10.15446/recolma.v52n2.77158

ACM

[1]
Fernández, V. y Murciano, C. 2018. Discriminant Structures Associated to Matrix Semantics. Revista Colombiana de Matemáticas. 52, 2 (jul. 2018), 185-209. DOI:https://doi.org/10.15446/recolma.v52n2.77158.

ACS

(1)
Fernández, V.; Murciano, C. Discriminant Structures Associated to Matrix Semantics. rev.colomb.mat 2018, 52, 185-209.

ABNT

FERNÁNDEZ, V.; MURCIANO, C. Discriminant Structures Associated to Matrix Semantics. Revista Colombiana de Matemáticas, [S. l.], v. 52, n. 2, p. 185-209, 2018. DOI: 10.15446/recolma.v52n2.77158. Disponível em: https://revistas.unal.edu.co/index.php/recolma/article/view/77158. Acesso em: 28 nov. 2021.

Chicago

Fernández, Víctor, y Carina Murciano. 2018. «Discriminant Structures Associated to Matrix Semantics». Revista Colombiana de Matemáticas 52 (2):185-209. https://doi.org/10.15446/recolma.v52n2.77158.

Harvard

Fernández, V. y Murciano, C. (2018) «Discriminant Structures Associated to Matrix Semantics», Revista Colombiana de Matemáticas, 52(2), pp. 185-209. doi: 10.15446/recolma.v52n2.77158.

IEEE

[1]
V. Fernández y C. Murciano, «Discriminant Structures Associated to Matrix Semantics», rev.colomb.mat, vol. 52, n.º 2, pp. 185-209, jul. 2018.

MLA

Fernández, V., y C. Murciano. «Discriminant Structures Associated to Matrix Semantics». Revista Colombiana de Matemáticas, vol. 52, n.º 2, julio de 2018, pp. 185-09, doi:10.15446/recolma.v52n2.77158.

Turabian

Fernández, Víctor, y Carina Murciano. «Discriminant Structures Associated to Matrix Semantics». Revista Colombiana de Matemáticas 52, no. 2 (julio 1, 2018): 185-209. Accedido noviembre 28, 2021. https://revistas.unal.edu.co/index.php/recolma/article/view/77158.

Vancouver

1.
Fernández V, Murciano C. Discriminant Structures Associated to Matrix Semantics. rev.colomb.mat [Internet]. 1 de julio de 2018 [citado 28 de noviembre de 2021];52(2):185-209. Disponible en: https://revistas.unal.edu.co/index.php/recolma/article/view/77158

Descargar cita

CrossRef Cited-by

CrossRef citations0

Dimensions

PlumX

Descargas

Los datos de descargas todavía no están disponibles.

Visitas a la página del resumen del artículo

223