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- Title
On a variety of hemi-implicative semilattices.
- Authors
Castiglioni, José Luis; Fernández, Víctor; Mallea, Héctor Federico; San Martín, Hernán Javier
- Abstract
A hemi-implicative semilattice is an algebra (A , ∧ , → , 1) of type (2, 2, 0) such that (A , ∧ , 1) is a bounded semilattice and the following conditions are satisfied: for every a , b , c ∈ A , if a ≤ b → c then a ∧ b ≤ c and for every a ∈ A , a → a = 1 . The class of hemi-implicative semilattices forms a variety. In this paper we introduce and study a proper subvariety of the variety of hemi-implicative semilattices, ShIS , which also properly contains some varieties of interest for algebraic logic. Our main goal is to show a representation theorem for ShIS . More precisely, we prove that every algebra of ShIS is isomorphic to a subalgebra of a member of ShIS whose underlying bounded semilattice is the bounded semilattice of upsets of a poset.
- Subjects
SEMILATTICES; ALGEBRAIC logic; DISTRIBUTIVE lattices; ALGEBRAIC varieties; ALGEBRA
- Publication
Soft Computing - A Fusion of Foundations, Methodologies & Applications, 2022, Vol 26, Issue 7, p3187
- ISSN
1432-7643
- Publication type
Article
- DOI
10.1007/s00500-022-06807-4