{"title":"在所有超实数集合中关于可忽略性和接近性的推理","authors":"Philippe Balbiani","doi":"10.1016/j.jal.2016.04.002","DOIUrl":null,"url":null,"abstract":"<div><p>We consider the binary relations of negligibility, comparability and proximity in the set of all hyperreals. Associating with negligibility, comparability and proximity the binary predicates <em>N</em>, <em>C</em> and <em>P</em> and the connectives <span><math><mo>[</mo><mi>N</mi><mo>]</mo></math></span>, <span><math><mo>[</mo><mi>C</mi><mo>]</mo></math></span> and <span><math><mo>[</mo><mi>P</mi><mo>]</mo></math></span>, we consider a first-order theory based on these predicates and a modal logic based on these connectives. We investigate the axiomatization/completeness and the decidability/complexity of this first-order theory and this modal logic.</p></div>","PeriodicalId":54881,"journal":{"name":"Journal of Applied Logic","volume":"16 ","pages":"Pages 14-36"},"PeriodicalIF":0.0000,"publicationDate":"2016-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.jal.2016.04.002","citationCount":"3","resultStr":"{\"title\":\"Reasoning about negligibility and proximity in the set of all hyperreals\",\"authors\":\"Philippe Balbiani\",\"doi\":\"10.1016/j.jal.2016.04.002\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We consider the binary relations of negligibility, comparability and proximity in the set of all hyperreals. Associating with negligibility, comparability and proximity the binary predicates <em>N</em>, <em>C</em> and <em>P</em> and the connectives <span><math><mo>[</mo><mi>N</mi><mo>]</mo></math></span>, <span><math><mo>[</mo><mi>C</mi><mo>]</mo></math></span> and <span><math><mo>[</mo><mi>P</mi><mo>]</mo></math></span>, we consider a first-order theory based on these predicates and a modal logic based on these connectives. We investigate the axiomatization/completeness and the decidability/complexity of this first-order theory and this modal logic.</p></div>\",\"PeriodicalId\":54881,\"journal\":{\"name\":\"Journal of Applied Logic\",\"volume\":\"16 \",\"pages\":\"Pages 14-36\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2016-07-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1016/j.jal.2016.04.002\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Applied Logic\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S157086831630012X\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Applied Logic","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S157086831630012X","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"Mathematics","Score":null,"Total":0}
Reasoning about negligibility and proximity in the set of all hyperreals
We consider the binary relations of negligibility, comparability and proximity in the set of all hyperreals. Associating with negligibility, comparability and proximity the binary predicates N, C and P and the connectives , and , we consider a first-order theory based on these predicates and a modal logic based on these connectives. We investigate the axiomatization/completeness and the decidability/complexity of this first-order theory and this modal logic.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
