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Discrete duality for 3-valued Łukasiewicz–Moisil algebras
- Source :
- Asian-European Journal of Mathematics. 10:1750003
- Publication Year :
- 2017
- Publisher :
- World Scientific Pub Co Pte Lt, 2017.
-
Abstract
- In 2011, Düntsch and Orlowska obtained a discrete duality for regular double Stone algebras. On the other hand, it is well known that regular double Stone algebras are polinominally equivalent to 3-valued Lukasiewicz-Moisil algebras (or LM3-algebras). In [R. Cignoli, Injective De Morgan and Kleene algebra, Proc. Amer. Math. Soc. 47 (1975) 269-278], LM3-algebras are considered as a Kleene algebras (L,∨,∧,∼, 0, 1) endowed with a unary operation : L → L, satisfying the properties: a∨ ∼ a = 1, ∼ a ∧ a = a∧ ∼ a and a∨b ≤(a ∨ b). Motivated by this result, in this paper, we determine another discrete duality for LM3-algebras, extending the discrete duality to De Morgan algebras described in [W. Dzik, E. Orlowska and C. van Alten, Relational representation theorems for general lattices with negations, in Relations and Kleene Algebra in Computer Science, Lecture Notes in Computer Science, Vol. 4136 (Springer, Berlin, 2006), pp. 162-176]. Fil: Pelaitay, Gustavo Andrés. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Juan; Argentina. Universidad Nacional de San Juan. Facultad de Filosofía, Humanidades y Artes; Argentina
- Subjects :
- Discrete mathematics
Pure mathematics
Unary operation
Matemáticas
General Mathematics
010102 general mathematics
Duality (optimization)
02 engineering and technology
01 natural sciences
Injective function
Matemática Pura
Kleene algebra
Negation
DE MORGAN ALGEBRAS
DISCRETE DUALITY
3 -VALUED LUKASIEWICZ-MOISIL ALGEBRAS
0202 electrical engineering, electronic engineering, information engineering
020201 artificial intelligence & image processing
0101 mathematics
Representation (mathematics)
CIENCIAS NATURALES Y EXACTAS
Mathematics
Subjects
Details
- ISSN :
- 17937183 and 17935571
- Volume :
- 10
- Database :
- OpenAIRE
- Journal :
- Asian-European Journal of Mathematics
- Accession number :
- edsair.doi.dedup.....e93dde457697098a5f7052317c519c8c