{"title":"Lambek-Grishin微积分的证明网","authors":"M. Moortgat, R. Moot","doi":"10.1093/acprof:oso/9780199646296.003.0010","DOIUrl":null,"url":null,"abstract":"Grishin's generalization of Lambek's Syntactic Calculus combines a non-commutative multiplicative conjunction and its residuals (product, left and right division) with a dual family: multiplicative disjunction, right and left difference. Interaction between these two families takes the form of linear distributivity principles. We study proof nets for the Lambek-Grishin calculus and the correspondence between these nets and unfocused and focused versions of its sequent calculus.","PeriodicalId":273067,"journal":{"name":"Quantum Physics and Linguistics","volume":"29 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2011-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"16","resultStr":"{\"title\":\"Proof nets for the Lambek-Grishin calculus\",\"authors\":\"M. Moortgat, R. Moot\",\"doi\":\"10.1093/acprof:oso/9780199646296.003.0010\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Grishin's generalization of Lambek's Syntactic Calculus combines a non-commutative multiplicative conjunction and its residuals (product, left and right division) with a dual family: multiplicative disjunction, right and left difference. Interaction between these two families takes the form of linear distributivity principles. We study proof nets for the Lambek-Grishin calculus and the correspondence between these nets and unfocused and focused versions of its sequent calculus.\",\"PeriodicalId\":273067,\"journal\":{\"name\":\"Quantum Physics and Linguistics\",\"volume\":\"29 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2011-12-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"16\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Quantum Physics and Linguistics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1093/acprof:oso/9780199646296.003.0010\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Quantum Physics and Linguistics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1093/acprof:oso/9780199646296.003.0010","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Grishin's generalization of Lambek's Syntactic Calculus combines a non-commutative multiplicative conjunction and its residuals (product, left and right division) with a dual family: multiplicative disjunction, right and left difference. Interaction between these two families takes the form of linear distributivity principles. We study proof nets for the Lambek-Grishin calculus and the correspondence between these nets and unfocused and focused versions of its sequent calculus.
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