{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,11]],"date-time":"2025-07-11T10:53:24Z","timestamp":1752231204913},"reference-count":9,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2006,11,13]],"date-time":"2006-11-13T00:00:00Z","timestamp":1163376000000},"content-version":"vor","delay-in-days":5430,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematical Logic Qtrly"],"published-print":{"date-parts":[[1992,1]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>In this paper we propose a new set of rules for a judgement calculus, i.e. a typed lambda calculus, based on Intuitionistic Linear Logic; these rules ease the problem of defining a suitable mathematical semantics. A proof of the canonical form theorem for this new system is given: it assures, beside the consistency of the calculus, the termination of the evaluation process of every well\u2010typed element. The definition of the mathematical semantics and a completeness theorem, that turns out to be a representation theorem, follow. This semantics is the basis to obtain a semantics for the evaluation process of every well\u2010typed program. 1991 MSC: 03B20, 03B40.<\/jats:p>","DOI":"10.1002\/malq.19920380105","type":"journal-article","created":{"date-parts":[[2007,5,29]],"date-time":"2007-05-29T05:46:42Z","timestamp":1180417602000},"page":"39-58","source":"Crossref","is-referenced-by-count":2,"title":["THE JUDGEMENT CALCULUS FOR INTUITIONISTIC LINEAR LOGIC: PROOF THEORY AND SEMANTICS"],"prefix":"10.1002","volume":"38","author":[{"given":"Silvio","family":"Valentini","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2006,11,13]]},"reference":[{"key":"e_1_2_1_2_2","unstructured":"Avron A. The semantics and proof theory of linear logic. In: Proceedings of the Workshop on Programming Logic (Dybjer Nordstrom Peterson Smith eds.) G\u00f6teborg1987."},{"key":"e_1_2_1_3_2","unstructured":"Abrusci V. M. Sequent calculus for Intuitionistic Linear Propositional Logic I II III. Preprint Dept. of Philosophy Univ. of Florence 1988."},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.1016\/0304-3975(87)90045-4"},{"key":"e_1_2_1_5_2","unstructured":"Girard J. I. andY.Lafont Intuitionistic Linear Logic. Proceedings of ICALP \u203287."},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.1016\/0304-3975(88)90100-4"},{"key":"e_1_2_1_7_2","first-page":"261","volume-title":"Proceedings of the Logic Colloquium 1988","author":"Sambin G.","year":"1989"},{"key":"e_1_2_1_8_2","first-page":"413","volume-title":"Proceedings of the Third Italian Conference of Theoretical Computer Science","author":"Solitro U.","year":"1989"},{"key":"e_1_2_1_9_2","unstructured":"Valentini S. A typed calculus based on quantifier free Intuitionistic Linear Logic. Preprint n. 59\/89 Dip. Scienze dell'Informazione. Univ. di Milano 1989."},{"key":"e_1_2_1_10_2","unstructured":"Valentini S. The judgement calculus for Intuitionistic Linear Logic: Proof theory and semantics. Preprint n. 64\/89 Dip. Scienze dell'Informazione Univ. di Milano 1989."}],"container-title":["Mathematical Logic Quarterly"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fmalq.19920380105","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/malq.19920380105","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,9,27]],"date-time":"2023-09-27T20:36:42Z","timestamp":1695847002000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/malq.19920380105"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1992,1]]},"references-count":9,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1992,1]]}},"alternative-id":["10.1002\/malq.19920380105"],"URL":"https:\/\/doi.org\/10.1002\/malq.19920380105","archive":["Portico"],"relation":{},"ISSN":["0942-5616","1521-3870"],"issn-type":[{"value":"0942-5616","type":"print"},{"value":"1521-3870","type":"electronic"}],"subject":[],"published":{"date-parts":[[1992,1]]}}}