{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,10]],"date-time":"2026-04-10T03:13:15Z","timestamp":1775790795792,"version":"3.50.1"},"reference-count":19,"publisher":"Cambridge University Press (CUP)","issue":"4","license":[{"start":{"date-parts":[[2009,3,4]],"date-time":"2009-03-04T00:00:00Z","timestamp":1236124800000},"content-version":"unspecified","delay-in-days":4598,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Struct. Comp. Sci."],"published-print":{"date-parts":[[1996,8]]},"abstract":"<jats:p>We continue our study of the negation-free structure of multiplicative linear logic, as represented by the structure of weakly distributive categories, to consider the \u2018exponentials\u2019! and ? in the weakly distributive context. In addition to the usual triple and cotriple structure that one would expect on each of the two operators, there must be some connection between them to replace the de Morgan relationship found in the linear logic context. This turns out to be the notion of tensorial strength. We analyze coherence for this situation, using a modification of the usual nets due to Danos, which is a form suitable for linear logic with exponentials but without negation.<\/jats:p>","DOI":"10.1017\/s0960129500001055","type":"journal-article","created":{"date-parts":[[2009,3,4]],"date-time":"2009-03-04T09:00:02Z","timestamp":1236157202000},"page":"313-351","source":"Crossref","is-referenced-by-count":9,"title":["! and ? \u2013 Storage as tensorial strength"],"prefix":"10.1017","volume":"6","author":[{"given":"R. F.","family":"Blute","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"J. R. B.","family":"Cockett","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"R. A. G.","family":"Seely","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2009,3,4]]},"reference":[{"key":"S0960129500001055_ref016","doi-asserted-by":"publisher","DOI":"10.1016\/0304-3975(94)00108-1"},{"key":"S0960129500001055_ref014","doi-asserted-by":"publisher","DOI":"10.1016\/0001-8708(91)90003-P"},{"key":"S0960129500001055_ref017","volume-title":"Natural Deduction","author":"Prawitz","year":"1965"},{"key":"S0960129500001055_ref006","doi-asserted-by":"publisher","DOI":"10.1017\/S0960129500000232"},{"key":"S0960129500001055_ref011","doi-asserted-by":"publisher","DOI":"10.1080\/00927877608822127"},{"key":"S0960129500001055_ref002","doi-asserted-by":"crossref","unstructured":"Benton B. N. , Bierman G. , de Paiva V. , AND Hyland M. , (1992) Term assignment for intuitionistic linear logic (preliminary report). Technical Report 262, University of Cambridge.","DOI":"10.1007\/BFb0037099"},{"key":"S0960129500001055_ref001","doi-asserted-by":"publisher","DOI":"10.1017\/S0960129500001274"},{"key":"S0960129500001055_ref019","unstructured":"Trimble T. H. (1994) Linear logic, bimodules, and full coherence for autonomous categories, Doctoral dissertation, Rutgers University."},{"key":"S0960129500001055_ref004","doi-asserted-by":"publisher","DOI":"10.1016\/0304-3975(93)90053-V"},{"key":"S0960129500001055_ref005","article-title":"Natural deduction and coherence for weakly distributive categories","author":"Blute","year":"1992","journal-title":"Journal of Pure and Applied Algebra"},{"key":"S0960129500001055_ref008","volume-title":"Proof theory for linear logics without negation","author":"Cockett","year":"1995"},{"key":"S0960129500001055_ref007","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511525902.004"},{"key":"S0960129500001055_ref009","unstructured":"Danos V. , (1990) La logique lin\u00e9aire appliqu\u00e9e \u00e0 l\u2019\u00e9tude de divers processus de normalisation et principalement du \u03bb-calcul, Doctoral dissertation, Universit\u00e9 de Paris."},{"key":"S0960129500001055_ref003","volume-title":"Proceedings of Conference on Typed lambda calculus and Applications","author":"Bierman","year":"1995"},{"key":"S0960129500001055_ref015","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0079385"},{"key":"S0960129500001055_ref012","doi-asserted-by":"publisher","DOI":"10.1016\/0304-3975(87)90045-4"},{"key":"S0960129500001055_ref018","doi-asserted-by":"publisher","DOI":"10.1090\/conm\/092\/1003210"},{"key":"S0960129500001055_ref010","doi-asserted-by":"publisher","DOI":"10.1007\/BF01622878"},{"key":"S0960129500001055_ref013","doi-asserted-by":"publisher","DOI":"10.1017\/S0960129500001328"}],"container-title":["Mathematical Structures in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0960129500001055","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,12]],"date-time":"2019-05-12T20:50:34Z","timestamp":1557694234000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0960129500001055\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1996,8]]},"references-count":19,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1996,8]]}},"alternative-id":["S0960129500001055"],"URL":"https:\/\/doi.org\/10.1017\/s0960129500001055","relation":{},"ISSN":["0960-1295","1469-8072"],"issn-type":[{"value":"0960-1295","type":"print"},{"value":"1469-8072","type":"electronic"}],"subject":[],"published":{"date-parts":[[1996,8]]}}}