{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,3]],"date-time":"2022-04-03T07:08:34Z","timestamp":1648969714091},"reference-count":9,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":2568,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2007,3]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We examine \u2018weak-distributivity\u2019 as a rewriting rule <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200005545_inline1\" \/> defined on multiplicative proofstructures (so, in particular, on multiplicative proof-nets: MLL). This rewriting does not preserve the type of proof-nets, but does nevertheless preserve their correctness. The specific contribution of this paper, is to give a direct proof of completeness for <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200005545_inline1\" \/>: starting from a set of simple generators (proof-nets which are a <jats:italic>n<\/jats:italic>-ary \u2297 of \u0551-ized axioms), any mono-conclusion MLL proof-net can be reached by <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200005545_inline1\" \/> rewriting (up to \u2297 and \u0551 associativity and commutativity).<\/jats:p>","DOI":"10.2178\/jsl\/1174668390","type":"journal-article","created":{"date-parts":[[2007,12,19]],"date-time":"2007-12-19T11:24:33Z","timestamp":1198063473000},"page":"159-170","source":"Crossref","is-referenced-by-count":0,"title":["Completeness of MLL proof-nets w.r.t. weak distributivity"],"prefix":"10.1017","volume":"72","author":[{"given":"Jean-Baptiste","family":"Joinet","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200005545_ref009","unstructured":"Retor\u00e9 C. , Handsome proof-nets: R&B graphs, perfect matchings and Series-Parallel graphs, Technical Report RR-36-52, INRIA, 1999."},{"key":"S0022481200005545_ref003","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-3975(01)00148-7"},{"key":"S0022481200005545_ref001","first-page":"230\u2013240","volume-title":"RTA 97","volume":"1232","author":"Bechet","year":"1997"},{"key":"S0022481200005545_ref004","first-page":"181\u2013203","article-title":"The structure of multiplicatives","volume":"28","author":"Danos","year":"1995","journal-title":"Archives for Mathematical Logic"},{"key":"S0022481200005545_ref006","doi-asserted-by":"publisher","DOI":"10.1016\/0304-3975(87)90045-4"},{"key":"S0022481200005545_ref002","unstructured":"Danos V. , La logique lin\u00e9aire appliqu\u00e9e \u00e0 l'etude de divers processus de normalisation (principalement du \u03bb-calcul), Ph.D. thesis, Universit\u00e9 Paris 7, 06 1990."},{"key":"S0022481200005545_ref005","first-page":"234\u2013242","volume-title":"Proceedings 14th Annual IEEE Symposium on Logic in Computer Science, LICS '99","author":"Devarajan","year":"1999"},{"key":"S0022481200005545_ref007","volume-title":"ACM Transactions on Computational Logic","author":"Guglielmi"},{"key":"S0022481200005545_ref008","doi-asserted-by":"publisher","DOI":"10.1007\/s00153-004-0242-2"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200005545","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,1]],"date-time":"2019-05-01T20:11:06Z","timestamp":1556741466000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200005545\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007,3]]},"references-count":9,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2007,3]]}},"alternative-id":["S0022481200005545"],"URL":"https:\/\/doi.org\/10.2178\/jsl\/1174668390","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2007,3]]}}}