{"title":"Sub-sub-intuitionistic logic","authors":"Jonte Deakin, Jim de Groot","doi":"arxiv-2408.12030","DOIUrl":null,"url":null,"abstract":"Sub-sub-intuitionistic logic is obtained from intuitionistic logic by\nweakening the implication and removing distributivity. It can alternatively be\nviewed as conditional weak positive logic. We provide semantics for\nsub-sub-intuitionistic logic by means of semilattices with a selection\nfunction, prove a categorical duality for the algebraic semantics of the logic,\nand use this to derive completeness. We then consider the extension of\nsub-sub-intuitionistic logic with a variety of axioms.","PeriodicalId":501306,"journal":{"name":"arXiv - MATH - Logic","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2024-08-21","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-2408.12030","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
Sub-sub-intuitionistic logic is obtained from intuitionistic logic by
weakening the implication and removing distributivity. It can alternatively be
viewed as conditional weak positive logic. We provide semantics for
sub-sub-intuitionistic logic by means of semilattices with a selection
function, prove a categorical duality for the algebraic semantics of the logic,
and use this to derive completeness. We then consider the extension of
sub-sub-intuitionistic logic with a variety of axioms.
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