On congruences in weak implicative semi-lattices
type: Item
instance of: scholarly article
title: On congruences in weak implicative semi-lattices
zbMATH Open document ID: 1403.06006
author: Hernán Javier San Martín
published in: Soft Computing
publication date: 2018-02-27T00:00:00Z
review text: The weak implicative semi-lattices are obtained from Heyting algebras \((H,\wedge,\vee,\rightarrow,0,1)\) by replacing the residuation property: \[ z\leq x\rightarrow y\text{ if and only if }x\wedge z\leq y \leqno{(R)} \] by its weaker form: \[ \text{if }z\leq x\rightarrow y,\text{ then }x\wedge z\leq y. \leqno{(R^{\prime})} \] The paper presents some properties of weak implicative semi-lattices and gives characterizations of congruences in this class of algebras, including varieties of interest for the logic.
Mathematics Subject Classification ID: 06B10
Mathematics Subject Classification ID: 06A12
Mathematics Subject Classification ID: 06D20
Mathematics Subject Classification ID: 03G25
Mathematics Subject Classification ID: 06D75
zbMATH DE Number: 6844105
zbMATH Keywords: semi-Heyting algebras
zbMATH Keywords: implicative semi-lattices
zbMATH Keywords: implication operation
zbMATH Keywords: congruence
zbMATH Keywords: compatible functions
zbMATH Keywords: locally affine completeness
reviewed by: Lavinia Ciungu
MaRDI profile type: Publication
full work available at URL: s00500-016-2188-9
OpenAlex ID: W2405703447
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DOI: 10.1007/S00500-016-2188-9
description: scientific article; zbMATH DE number 6844105