{"title":"Two-variable logic with counting is decidable","authors":"E. Grädel, M. Otto, Eric Rosen","doi":"10.1109/LICS.1997.614957","DOIUrl":null,"url":null,"abstract":"We prove that the satisfiability and the finite satisfiability problems for C/sup 2/ are decidable. C/sup 2/ is first-order logic with only two variables in the presence of arbitrary counting quantifiers 3/sup /spl ges/m/,m/spl ges/1. It considerably extends L/sup 2/ plain first-order with only two variables, which is known to be decidable by a result of Mortimer's. Unlike L/sup 2/, C/sup 2/ does not have the finite model property.","PeriodicalId":272903,"journal":{"name":"Proceedings of Twelfth Annual IEEE Symposium on Logic in Computer Science","volume":"1 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1997-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"206","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of Twelfth Annual IEEE Symposium on Logic in Computer Science","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/LICS.1997.614957","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 206
Abstract
We prove that the satisfiability and the finite satisfiability problems for C/sup 2/ are decidable. C/sup 2/ is first-order logic with only two variables in the presence of arbitrary counting quantifiers 3/sup /spl ges/m/,m/spl ges/1. It considerably extends L/sup 2/ plain first-order with only two variables, which is known to be decidable by a result of Mortimer's. Unlike L/sup 2/, C/sup 2/ does not have the finite model property.
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