Sesión Lógica y Computabilidad$NS_{3\times 3}$-algebras and symmetrical Heyting algebras
CARLOS GALLARDO
DEPARTAMENTO DE MATEMÁTICA. UNIVERSIDAD NACIONAL DEL SUR, ARGENTINA - Esta dirección de correo electrónico está siendo protegida contra los robots de spam. Necesita tener JavaScript habilitado para poder verlo.
The notion of $n\times m$--valued {\L}ukasiewicz algebras with negation (or $NS_{n \times m}$-algebras) was introduced by C. Sanza in [4]. In this note, we focus on $NS_{3 \times 3}$-algebras. We prove that they are Heyting algebras and in case that they are centered we describe the Heyting implication in terms of their centers. We also establish a relationship between centered $NS_{3 \times 3}$-algebras and a class of symmetrical Heyting algebras with operators.
Referencias
[1] Gallardo, C. and Ziliani, A.: Symmetrical Heyting algebras of order $3\times 3$. Soft Computing., 25, 2, 8839–-8847 (2021).
[2] Iturrioz, L.: \L ukasiewicz and symmetrical Heyting algebras}. Zeitschr. f. math. Logik und Grundlagen d. Math. 23, 131--136 (1977).
[3] Iturrioz, L.: Modal operators on symmetrical Heyting algebras}. Banach Center Publications 9, Universal algebra and applications, 289–-303 (1982).
[4] Sanza, C.: Notes on $n\times m$--valued \L ukasiewicz Algebras with Negation. Logic J. of the IGPL 6, 12, 499--507 (2004).