{"title":"在有限偏序集上定义的所有单调偏函数集合的有限基","authors":"A. Nozaki, Vaktang Lashkia","doi":"10.1109/ISMVL.1998.679518","DOIUrl":null,"url":null,"abstract":"Let X be an arbitrary poset. A partial function f with n variables defined over X is said to be monotone if the following condition is satisfied: if x/sub 1//spl les/y/sub 1/,..., x/sub m//spl les/y/sub n/, and both the values f(x/sub 1/,..., x/sub n/) and f(y/sub 1/,....y/sub n/) are defined, then f(x/sub 1/,..., x/sub n/)/spl les/f(y/sub 1/,...,y/sub n/) It is shown that the set of all monotone partial functions has a finite basis.","PeriodicalId":377860,"journal":{"name":"Proceedings. 1998 28th IEEE International Symposium on Multiple- Valued Logic (Cat. No.98CB36138)","volume":"36 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1998-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"A finite basis of the set of all monotone partial functions defined over a finite poset\",\"authors\":\"A. Nozaki, Vaktang Lashkia\",\"doi\":\"10.1109/ISMVL.1998.679518\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let X be an arbitrary poset. A partial function f with n variables defined over X is said to be monotone if the following condition is satisfied: if x/sub 1//spl les/y/sub 1/,..., x/sub m//spl les/y/sub n/, and both the values f(x/sub 1/,..., x/sub n/) and f(y/sub 1/,....y/sub n/) are defined, then f(x/sub 1/,..., x/sub n/)/spl les/f(y/sub 1/,...,y/sub n/) It is shown that the set of all monotone partial functions has a finite basis.\",\"PeriodicalId\":377860,\"journal\":{\"name\":\"Proceedings. 1998 28th IEEE International Symposium on Multiple- Valued Logic (Cat. No.98CB36138)\",\"volume\":\"36 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1998-05-27\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings. 1998 28th IEEE International Symposium on Multiple- Valued Logic (Cat. No.98CB36138)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/ISMVL.1998.679518\",\"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. 1998 28th IEEE International Symposium on Multiple- Valued Logic (Cat. No.98CB36138)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ISMVL.1998.679518","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A finite basis of the set of all monotone partial functions defined over a finite poset
Let X be an arbitrary poset. A partial function f with n variables defined over X is said to be monotone if the following condition is satisfied: if x/sub 1//spl les/y/sub 1/,..., x/sub m//spl les/y/sub n/, and both the values f(x/sub 1/,..., x/sub n/) and f(y/sub 1/,....y/sub n/) are defined, then f(x/sub 1/,..., x/sub n/)/spl les/f(y/sub 1/,...,y/sub n/) It is shown that the set of all monotone partial functions has a finite basis.
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