{"title":"A mixed logic with binary operators","authors":"Ivo Düntsch, Rafał Gruszczyński, Paula Menchón","doi":"arxiv-2408.09581","DOIUrl":null,"url":null,"abstract":"In previous work \"Betweenness algebras\" we introduced and examined the class\nof betweenness algebras. In the current paper we study a larger class of\nalgebras with binary operators of possibility and sufficiency, the weak mixed\nalgebras. Furthermore, we develop a system of logic with two binary modalities,\nsound and complete with respect to the class of frames closely related to the\naforementioned algebras, and we prove an embedding theorem which solves an open\nproblem from \"Betweenness algebras\".","PeriodicalId":501306,"journal":{"name":"arXiv - MATH - Logic","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2024-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Logic","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2408.09581","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
In previous work "Betweenness algebras" we introduced and examined the class
of betweenness algebras. In the current paper we study a larger class of
algebras with binary operators of possibility and sufficiency, the weak mixed
algebras. Furthermore, we develop a system of logic with two binary modalities,
sound and complete with respect to the class of frames closely related to the
aforementioned algebras, and we prove an embedding theorem which solves an open
problem from "Betweenness algebras".
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