{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:06:23Z","timestamp":1760058383798,"version":"build-2065373602"},"reference-count":24,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2025,3,28]],"date-time":"2025-03-28T00:00:00Z","timestamp":1743120000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Key Project of Chinese Ministry of Education","award":["22JJD720021","23YJC72040003"],"award-info":[{"award-number":["22JJD720021","23YJC72040003"]}]},{"name":"Chinese Ministry of Education of Humanities and Social Science Project","award":["22JJD720021","23YJC72040003"],"award-info":[{"award-number":["22JJD720021","23YJC72040003"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>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.<\/jats:p>","DOI":"10.3390\/axioms14040257","type":"journal-article","created":{"date-parts":[[2025,3,28]],"date-time":"2025-03-28T13:36:49Z","timestamp":1743169009000},"page":"257","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["On the Equational Theory of Lattice-Based Algebras for Layered Graphs"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8763-4473","authenticated-orcid":false,"given":"Zhe","family":"Yu","sequence":"first","affiliation":[{"name":"Department of Philosophy, Institute of Logic and Cognition, Sun Yat-sen University, Guangzhou 510275, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0469-3716","authenticated-orcid":false,"given":"Hao","family":"Zhan","sequence":"additional","affiliation":[{"name":"Department of Philosophy, Xiamen University, Xiamen 361005, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5975-2333","authenticated-orcid":false,"given":"Yiheng","family":"Wang","sequence":"additional","affiliation":[{"name":"Department of Philosophy, Institute of Logic and Cognition, Sun Yat-sen University, Guangzhou 510275, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhe","family":"Lin","sequence":"additional","affiliation":[{"name":"Department of Philosophy, Xiamen University, Xiamen 361005, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0006-3197-1565","authenticated-orcid":false,"given":"Fei","family":"Liang","sequence":"additional","affiliation":[{"name":"School of Philosophy and Social Development, Institute of Concept and Reasoning, Shandong University, Jinan 250061, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,3,28]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"469","DOI":"10.1007\/BF01195378","article-title":"Relation algebras as residuated Boolean algebras","volume":"30","author":"Tsinakis","year":"1993","journal-title":"Algebra Universalis"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"953","DOI":"10.1093\/logcom\/exu002","article-title":"A substructural logic for layered graphs","volume":"24","author":"Collinson","year":"2014","journal-title":"J. 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