{"title":"寓言:可决性与图同态","authors":"D. Pous, Valeria Vignudelli","doi":"10.1145/3209108.3209172","DOIUrl":null,"url":null,"abstract":"Allegories were introduced by Freyd and Scedrov; they form a fragment of Tarski's calculus of relations. We show that their equational theory is decidable by characterising it in terms of a specific class of graph homomorphisms. We actually do so for an extension of allegories which we prove to be conservative: allegories with top. This makes it possible to exploit a correspondence between terms and K4-free graphs, for which isomorphisms were known to be finitely axiomatisable.","PeriodicalId":389131,"journal":{"name":"Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science","volume":"10 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2018-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"7","resultStr":"{\"title\":\"Allegories: decidability and graph homomorphisms\",\"authors\":\"D. Pous, Valeria Vignudelli\",\"doi\":\"10.1145/3209108.3209172\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Allegories were introduced by Freyd and Scedrov; they form a fragment of Tarski's calculus of relations. We show that their equational theory is decidable by characterising it in terms of a specific class of graph homomorphisms. We actually do so for an extension of allegories which we prove to be conservative: allegories with top. This makes it possible to exploit a correspondence between terms and K4-free graphs, for which isomorphisms were known to be finitely axiomatisable.\",\"PeriodicalId\":389131,\"journal\":{\"name\":\"Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science\",\"volume\":\"10 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2018-07-09\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"7\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1145/3209108.3209172\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1145/3209108.3209172","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Allegories were introduced by Freyd and Scedrov; they form a fragment of Tarski's calculus of relations. We show that their equational theory is decidable by characterising it in terms of a specific class of graph homomorphisms. We actually do so for an extension of allegories which we prove to be conservative: allegories with top. This makes it possible to exploit a correspondence between terms and K4-free graphs, for which isomorphisms were known to be finitely axiomatisable.
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