Discriminant Structures Associated to Matrix Semantics

Fernández, Víctor; Murciano, Carina; Fernández, Víctor; Murciano, Carina

doi:10.15446/recolma.v52n2.77158

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Revista Colombiana de Matemáticas

Print version ISSN 0034-7426

Rev.colomb.mat. vol.52 no.2 Bogotá Jul./Dec. 2018

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

Original articles

Discriminant Structures Associated to Matrix Semantics

Estructuras Discriminantes Asociadas a Semánticas Matriciales

Víctor Fernández¹^*

Carina Murciano²

^¹ Universidad Nacional de San Juan, Instituto en Ciencias Básicas (Área Matemática) Av. José Ignacio de la Roza 230 (Oeste) San Juan, Argentina. e-mail: vlfernan@ffha.unsj.edu.ar

^² Universidad Nacional de San Juan, Instituto en Ciencias Básicas (Área Matemática) Av. José Ignacio de la Roza 230 (Oeste) San Juan, Argentina. e-mail: carimurciano@yahoo.com.ar.

Abstract

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 S _M 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.

Keywords: Matrix Logic; n-valued logics; Discriminant Structures

Resumen

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 S _M 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.

Palabras clave: Lógica Matricial; lógicas n-valuadas; Estructuras Discriminantes

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Referencias

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Received: February 13, 2018; Accepted: June 05, 2018

^* Correspondencia: Víctor Fernández, Instituto en Ciencias Básicas (Área Matemática), Universidad Nacional de San Juan, Av. José Ignacio de la Roza 230 (Oeste), San Juan, Argentina. Correo electrónico: vlfernan@ffha.unsj.edu.ar.

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