{"title":"超克隆的伽罗瓦连接","authors":"Hajime Machida, J. Pantović, I. Rosenberg","doi":"10.1109/ISMVL.2010.45","DOIUrl":null,"url":null,"abstract":"This paper is inspired by the paper of Tarasov in which he investigates maximal partial clones on a two-element set. It happens that the approach of Tarasov can be translated into the language of hyperclone theory. He introduced a notion of quasicomposition which assigns to extended hyperoperations extension of their composition. We introduce a new operation in the set of extended hyperoperation and define a quasiclone as a composition closed set of extended hyperoperations containing all projections which is closed with respect to the new operation. For a Galois connection between sets of extended hyperoperations and power relations, we prove that the set of all extended hyperoperations e-preserving every relation is a quasiclone and that each quasiclone is of the form ePolR for a set R of relations on the power set of A without empty-set. Finally, we re-state results of Tarasov in hyperclone framework.","PeriodicalId":447743,"journal":{"name":"2010 40th IEEE International Symposium on Multiple-Valued Logic","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2010-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"Galois Connection for Hyperclones\",\"authors\":\"Hajime Machida, J. Pantović, I. Rosenberg\",\"doi\":\"10.1109/ISMVL.2010.45\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This paper is inspired by the paper of Tarasov in which he investigates maximal partial clones on a two-element set. It happens that the approach of Tarasov can be translated into the language of hyperclone theory. He introduced a notion of quasicomposition which assigns to extended hyperoperations extension of their composition. We introduce a new operation in the set of extended hyperoperation and define a quasiclone as a composition closed set of extended hyperoperations containing all projections which is closed with respect to the new operation. For a Galois connection between sets of extended hyperoperations and power relations, we prove that the set of all extended hyperoperations e-preserving every relation is a quasiclone and that each quasiclone is of the form ePolR for a set R of relations on the power set of A without empty-set. Finally, we re-state results of Tarasov in hyperclone framework.\",\"PeriodicalId\":447743,\"journal\":{\"name\":\"2010 40th IEEE International Symposium on Multiple-Valued Logic\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2010-05-26\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2010 40th IEEE International Symposium on Multiple-Valued Logic\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/ISMVL.2010.45\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2010 40th IEEE International Symposium on Multiple-Valued Logic","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ISMVL.2010.45","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
This paper is inspired by the paper of Tarasov in which he investigates maximal partial clones on a two-element set. It happens that the approach of Tarasov can be translated into the language of hyperclone theory. He introduced a notion of quasicomposition which assigns to extended hyperoperations extension of their composition. We introduce a new operation in the set of extended hyperoperation and define a quasiclone as a composition closed set of extended hyperoperations containing all projections which is closed with respect to the new operation. For a Galois connection between sets of extended hyperoperations and power relations, we prove that the set of all extended hyperoperations e-preserving every relation is a quasiclone and that each quasiclone is of the form ePolR for a set R of relations on the power set of A without empty-set. Finally, we re-state results of Tarasov in hyperclone framework.