{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,19]],"date-time":"2025-06-19T04:27:48Z","timestamp":1750307268667,"version":"3.41.0"},"reference-count":25,"publisher":"Association for Computing Machinery (ACM)","issue":"4","license":[{"start":{"date-parts":[[2011,7,1]],"date-time":"2011-07-01T00:00:00Z","timestamp":1309478400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Comput. Logic"],"published-print":{"date-parts":[[2011,7]]},"abstract":"<jats:p>\n            We study a system, called NEL, which is the mixed commutative\/noncommutative linear logic BV augmented with linear logic's exponentials. Equivalently, NEL is MELL augmented with the noncommutative self-dual connective seq. In this article, we show a basic compositionality property of NEL, which we call\n            <jats:italic>decomposition<\/jats:italic>\n            . This result leads to a cut-elimination theorem, which is proved in the next article of this series. To control the induction measure for the theorem, we rely on a novel technique that extracts from NEL proofs the structure of exponentials, into what we call !-?-Flow-Graphs.\n          <\/jats:p>","DOI":"10.1145\/1970398.1970399","type":"journal-article","created":{"date-parts":[[2011,7,21]],"date-time":"2011-07-21T13:27:09Z","timestamp":1311254829000},"page":"1-39","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":5,"title":["A system of interaction and structure IV"],"prefix":"10.1145","volume":"12","author":[{"given":"Lutz Stra\u00df","family":"Burger","sequence":"first","affiliation":[{"name":"INRIA Saclay--\u00cele-de-France and \u00c9cole Polytechnique, France"}]},{"given":"Alessio","family":"Guglielmi","sequence":"additional","affiliation":[{"name":"University of Bath and INRIA Nancy--Grand Est, United Kingdom"}]}],"member":"320","published-online":{"date-parts":[[2011,7,22]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.2307\/2275407"},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0168-0072(99)00014-7"},{"key":"e_1_2_1_3_1","doi-asserted-by":"crossref","unstructured":"Blute R. Panangaden P. and Slavnov S. 2011. Deep inference and probablistic coherence spaces. Applied Categor. Struct. (To appear).  Blute R. Panangaden P. and Slavnov S. 2011. Deep inference and probablistic coherence spaces. Applied Categor. Struct. (To appear).","DOI":"10.1007\/s10485-010-9241-0"},{"key":"e_1_2_1_4_1","doi-asserted-by":"publisher","DOI":"10.1007\/11780342_7"},{"volume":"2250","volume-title":"Proceedings of the Conference on Logic for Programming, Artificial Intelligence, and Reasoning (LPAR'01)","author":"Br\u00fcnnler K.","key":"e_1_2_1_5_1"},{"key":"e_1_2_1_6_1","doi-asserted-by":"publisher","DOI":"10.1145\/1462179.1462186"},{"key":"e_1_2_1_7_1","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(91)90059-U"},{"key":"e_1_2_1_8_1","doi-asserted-by":"publisher","DOI":"10.1017\/S0960129500000451"},{"key":"e_1_2_1_9_1","doi-asserted-by":"publisher","DOI":"10.1016\/0304-3975(87)90045-4"},{"volume-title":"Linear Logic in Computer Science, T. Ehrhard, J.-Y","author":"Girard J.-Y.","key":"e_1_2_1_10_1"},{"key":"e_1_2_1_11_1","doi-asserted-by":"publisher","DOI":"10.1145\/1182613.1182614"},{"key":"e_1_2_1_12_1","doi-asserted-by":"crossref","unstructured":"Guglielmi A. and Gundersen T. 2008. Normalisation control in deep inference via atomic flows. Log. Meth. Comput. Sci. 4 1 9 1--36.  Guglielmi A. and Gundersen T. 2008. Normalisation control in deep inference via atomic flows. Log. Meth. Comput. Sci. 4 1 9 1--36.","DOI":"10.2168\/LMCS-4(1:9)2008"},{"volume":"2142","volume-title":"Proceedings of the Conference on Computer Science Logic (CSL'01)","author":"Guglielmi A.","key":"e_1_2_1_13_1"},{"volume":"2514","volume-title":"Proceedings of the Conference on Logic for Programming, Artificial Intelligence, and Reasoning (LPAR'02)","author":"Guglielmi A.","key":"e_1_2_1_14_1"},{"key":"e_1_2_1_15_1","doi-asserted-by":"publisher","DOI":"10.1017\/S096012951100003X"},{"key":"e_1_2_1_16_1","unstructured":"Retor\u00e9 C. 1993. R\u00e9seaux et s\u00e9quents ordonn\u00e9s. Ph.D. dissertation Universit\u00e9 Paris VII.  Retor\u00e9 C. 1993. R\u00e9seaux et s\u00e9quents ordonn\u00e9s. Ph.D. dissertation Universit\u00e9 Paris VII."},{"key":"e_1_2_1_17_1","doi-asserted-by":"publisher","DOI":"10.5555\/645893.671608"},{"volume-title":"Dynamic Perspectives in Logic and Linguistics","author":"Retor\u00e9 C.","key":"e_1_2_1_18_1"},{"key":"e_1_2_1_19_1","doi-asserted-by":"publisher","DOI":"10.5555\/645711.664616"},{"key":"e_1_2_1_20_1","unstructured":"Strassburger L. 2003a. Linear logic and noncommutativity in the calculus of structures. Ph.D. dissertation Technische Universit\u00e4t Dresden.  Strassburger L. 2003a. Linear logic and noncommutativity in the calculus of structures. Ph.D. dissertation Technische Universit\u00e4t Dresden."},{"key":"e_1_2_1_21_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-3975(03)00240-8"},{"key":"e_1_2_1_22_1","doi-asserted-by":"publisher","DOI":"10.1016\/S1571-0661(04)80853-3"},{"volume-title":"Structures and Deduction (Satellite Workshop of ICALP'05)","year":"2005","author":"Strassburger L.","key":"e_1_2_1_23_1"},{"key":"e_1_2_1_24_1","doi-asserted-by":"publisher","DOI":"10.2168\/LMCS-2(2:4)2006"},{"key":"e_1_2_1_25_1","doi-asserted-by":"publisher","DOI":"10.2307\/2274953"}],"container-title":["ACM Transactions on Computational Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1970398.1970399","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/1970398.1970399","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T10:52:53Z","timestamp":1750243973000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1970398.1970399"}},"subtitle":["The exponentials and decomposition"],"short-title":[],"issued":{"date-parts":[[2011,7]]},"references-count":25,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2011,7]]}},"alternative-id":["10.1145\/1970398.1970399"],"URL":"https:\/\/doi.org\/10.1145\/1970398.1970399","relation":{},"ISSN":["1529-3785","1557-945X"],"issn-type":[{"type":"print","value":"1529-3785"},{"type":"electronic","value":"1557-945X"}],"subject":[],"published":{"date-parts":[[2011,7]]},"assertion":[{"value":"2009-03-01","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2010-06-01","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2011-07-22","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}