On the Equational Theory of Lattice-Based Algebras for Layered Graphs

Layered algebras are introduced and used to express layered graphs. Layered graphs are considered to be a highly effective abstract tool to manage the difficulty in conceptualizing and reasoning regarding complex systems related to coding in email exchange and access control in security. In the pres...

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Main Authors: Zhe Yu, Hao Zhan, Yiheng Wang, Zhe Lin, Fei Liang
Format: Article
Language:English
Published: MDPI AG 2025-03-01
Series:Axioms
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Online Access:https://www.mdpi.com/2075-1680/14/4/257
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author Zhe Yu
Hao Zhan
Yiheng Wang
Zhe Lin
Fei Liang
author_facet Zhe Yu
Hao Zhan
Yiheng Wang
Zhe Lin
Fei Liang
author_sort Zhe Yu
collection DOAJ
description Layered algebras are introduced and used to express layered graphs. Layered graphs are considered to be a highly effective abstract tool to manage the difficulty in conceptualizing and reasoning regarding complex systems related to coding in email exchange and access control in security. In the present paper, we study the varieties of several classes of lattice-based layer algebras and show that all these varieties have decidable equational theory via a finite model property.
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spelling doaj-art-e7b37389e10649a99211cdc01f392fb92025-08-20T02:17:14ZengMDPI AGAxioms2075-16802025-03-0114425710.3390/axioms14040257On the Equational Theory of Lattice-Based Algebras for Layered GraphsZhe Yu0Hao Zhan1Yiheng Wang2Zhe Lin3Fei Liang4Department of Philosophy, Institute of Logic and Cognition, Sun Yat-sen University, Guangzhou 510275, ChinaDepartment of Philosophy, Xiamen University, Xiamen 361005, ChinaDepartment of Philosophy, Institute of Logic and Cognition, Sun Yat-sen University, Guangzhou 510275, ChinaDepartment of Philosophy, Xiamen University, Xiamen 361005, ChinaSchool of Philosophy and Social Development, Institute of Concept and Reasoning, Shandong University, Jinan 250061, ChinaLayered algebras are introduced and used to express layered graphs. Layered graphs are considered to be a highly effective abstract tool to manage the difficulty in conceptualizing and reasoning regarding complex systems related to coding in email exchange and access control in security. In the present paper, we study the varieties of several classes of lattice-based layer algebras and show that all these varieties have decidable equational theory via a finite model property.https://www.mdpi.com/2075-1680/14/4/257layered algebraslayered graphresiduated groupoidresiduated latticeequational theoryvariety
spellingShingle Zhe Yu
Hao Zhan
Yiheng Wang
Zhe Lin
Fei Liang
On the Equational Theory of Lattice-Based Algebras for Layered Graphs
Axioms
layered algebras
layered graph
residuated groupoid
residuated lattice
equational theory
variety
title On the Equational Theory of Lattice-Based Algebras for Layered Graphs
title_full On the Equational Theory of Lattice-Based Algebras for Layered Graphs
title_fullStr On the Equational Theory of Lattice-Based Algebras for Layered Graphs
title_full_unstemmed On the Equational Theory of Lattice-Based Algebras for Layered Graphs
title_short On the Equational Theory of Lattice-Based Algebras for Layered Graphs
title_sort on the equational theory of lattice based algebras for layered graphs
topic layered algebras
layered graph
residuated groupoid
residuated lattice
equational theory
variety
url https://www.mdpi.com/2075-1680/14/4/257
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AT feiliang ontheequationaltheoryoflatticebasedalgebrasforlayeredgraphs