INVESTIGADORES
SAN MARTIN Hernan Javier
artículos
Título:
On weak Lewis distributive lattices
Autor/es:
CALOMINO ISMAEL; CELANI SERGIO ARTURO; SAN MARTÍN HERNÁN JAVIER
Revista:
STUDIA LOGICA
Editorial:
Springer
Referencias:
Año: 2024
ISSN:
0039-3215
Resumen:
In this paper we study the variety WL of bounded distributive lattices endowed with an implication, called weak Lewis distributive lattices. This variety corresponds to the algebraic semantics of the supremum-infimum-implicative-0-1-fragment of the arithmetical base preservativity logic iP-. The variety WL properly contains the variety of bounded distributive lattices with strict implication, also known as weak Heyting algebras. We introduce the notion of WL-frame and we prove a representation theorem for WL-lattices by means of WL-frames. We extended this representation to a topological duality by means of Priestley spaces endowed with a special neighbourhood relation between points and closed upsets of the space. These results are applied in order to give a representation and a topological duality for the variety of weak Heyting-Lewis algebras, i.e., for the algebraic semantics of the arithmetical base preservativity logic iP-.
