{"title":"Representable and diagonally representable weakening relation algebras","authors":"P. Jipsen, Jas Semrl","doi":"10.48550/arXiv.2301.02213","DOIUrl":"https://doi.org/10.48550/arXiv.2301.02213","url":null,"abstract":"A binary relation defined on a poset is a weakening relation if the partial order acts as a both-sided compositional identity. This is motivated by the weakening rule in sequent calculi and closely related to models of relevance logic. For a fixed poset the collection of weakening relations is a subreduct of the full relation algebra on the underlying set of the poset. We present a two-player game for the class of representable weakening relation algebras akin to that for the class of representable relation algebras. This enables us to define classes of abstract weakening relation algebras that approximate the quasivariety of representable weakening relation algebras. We give explicit finite axiomatisations for some of these classes. We define the class of diagonally representable weakening relation algebras and prove that it is a discriminator variety. We also provide explicit representations for several small weakening relation algebras.","PeriodicalId":273640,"journal":{"name":"International Conference on Relational and Algebraic Methods in Computer Science","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129815146","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Implication Algebras and Implication Semigroups of Binary Relations","authors":"Andrew Lewis-Smith, Jas Semrl","doi":"10.1007/978-3-031-28083-2_12","DOIUrl":"https://doi.org/10.1007/978-3-031-28083-2_12","url":null,"abstract":"","PeriodicalId":273640,"journal":{"name":"International Conference on Relational and Algebraic Methods in Computer Science","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134481572","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Some modal and temporal translations of generalized basic logic","authors":"Wesley Fussner, W. Z. Botero","doi":"10.1007/978-3-030-88701-8_11","DOIUrl":"https://doi.org/10.1007/978-3-030-88701-8_11","url":null,"abstract":"","PeriodicalId":273640,"journal":{"name":"International Conference on Relational and Algebraic Methods in Computer Science","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122021318","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Domain Range Semigroups and Finite Representations","authors":"Jas Semrl","doi":"10.1007/978-3-030-88701-8_29","DOIUrl":"https://doi.org/10.1007/978-3-030-88701-8_29","url":null,"abstract":"","PeriodicalId":273640,"journal":{"name":"International Conference on Relational and Algebraic Methods in Computer Science","volume":"749 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115133459","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Computing Least and Greatest Fixed Points in Absorptive Semirings","authors":"Matthias Naaf","doi":"10.1007/978-3-030-88701-8_21","DOIUrl":"https://doi.org/10.1007/978-3-030-88701-8_21","url":null,"abstract":"","PeriodicalId":273640,"journal":{"name":"International Conference on Relational and Algebraic Methods in Computer Science","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116687195","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Agi Kurucz, V. Ryzhikov, Yury Savateev, M. Zakharyaschev
{"title":"Deciding FO-definability of Regular Languages","authors":"Agi Kurucz, V. Ryzhikov, Yury Savateev, M. Zakharyaschev","doi":"10.1007/978-3-030-88701-8_15","DOIUrl":"https://doi.org/10.1007/978-3-030-88701-8_15","url":null,"abstract":"","PeriodicalId":273640,"journal":{"name":"International Conference on Relational and Algebraic Methods in Computer Science","volume":"638 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122952482","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Accretive Computation of Global Transformations","authors":"A. Fernandez, Luidnel Maignan, Antoine Spicher","doi":"10.1007/978-3-030-88701-8_10","DOIUrl":"https://doi.org/10.1007/978-3-030-88701-8_10","url":null,"abstract":"","PeriodicalId":273640,"journal":{"name":"International Conference on Relational and Algebraic Methods in Computer Science","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129727344","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Comer Schemes, Relation Algebras, and the Flexible Atom Conjecture","authors":"Jeremy F. Alm, David A. Andrews, Michael Levet","doi":"10.1007/978-3-031-28083-2_2","DOIUrl":"https://doi.org/10.1007/978-3-031-28083-2_2","url":null,"abstract":"","PeriodicalId":273640,"journal":{"name":"International Conference on Relational and Algebraic Methods in Computer Science","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116820619","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Algebraic Derivation of Until Rules and Application to Timer Verification","authors":"Jessica Ertel, Roland Glück, B. Möller","doi":"10.1007/978-3-030-02149-8_15","DOIUrl":"https://doi.org/10.1007/978-3-030-02149-8_15","url":null,"abstract":"","PeriodicalId":273640,"journal":{"name":"International Conference on Relational and Algebraic Methods in Computer Science","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116124737","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}