{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,1]],"date-time":"2022-04-01T14:59:51Z","timestamp":1648825191734},"reference-count":9,"publisher":"Cambridge University Press (CUP)","issue":"2","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":4302,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2002,6]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Each Girard quantale (i.e., commutative quantale with a selected dualizing element) provides a support for a semantics for linear propositional formulas (but not for linear derivations). Several constructions of Girard quantales are known. We give two more constructions, one using an arbitrary partially ordered monoid and one using a partially ordered group (both commutative). In both cases the semantics can be controlled be a relation between pairs of elements of the support and formulas. This gives us a neat way of handling duality.<\/jats:p>","DOI":"10.2178\/jsl\/1190150094","type":"journal-article","created":{"date-parts":[[2007,12,13]],"date-time":"2007-12-13T14:13:31Z","timestamp":1197555211000},"page":"505-527","source":"Crossref","is-referenced-by-count":0,"title":["Monoid based semantics for linear formulas (corrected republication)"],"prefix":"10.1017","volume":"67","author":[{"given":"W. P. R.","family":"Mitchell","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"H.","family":"Simmons","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200009580_ref005","first-page":"99","volume":"12","author":"Mulvey","year":"1986","journal-title":"Rendiconti del Circolo Matematico di Palermo. Ser II Supplemento"},{"key":"S0022481200009580_ref009","unstructured":"Yetter D. , Quantales and (non-commutative) linear logic, this Journal, (1990), pp. 41\u201364."},{"key":"S0022481200009580_ref004","volume-title":"London mathematical society lecture notes series","volume":"222","author":"Girard","year":"1995"},{"key":"S0022481200009580_ref003","first-page":"1","volume-title":"Theoretical Computer Science","author":"Girard","year":"1987"},{"key":"S0022481200009580_ref001","unstructured":"Ambler S. , First order linear logic in symmetric monoidal closed categories, Ph.D. thesis , University of Edinburgh, 1991."},{"key":"S0022481200009580_ref008","volume-title":"CSLI lectures notes","author":"Troelstra","year":"1992"},{"key":"S0022481200009580_ref002","unstructured":"de Paiva V. , Categorical proof theory and linear logic, can be found in http:\/\/www.cs.bham.ac.uk\/vdp."},{"key":"S0022481200009580_ref007","doi-asserted-by":"publisher","DOI":"10.1090\/conm\/092\/1003210"},{"key":"S0022481200009580_ref006","volume-title":"Pitman research notes in mathematics","author":"Rosenthal","year":"1990"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200009580","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,6]],"date-time":"2019-05-06T21:05:57Z","timestamp":1557176757000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200009580\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2002,6]]},"references-count":9,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2002,6]]}},"alternative-id":["S0022481200009580"],"URL":"https:\/\/doi.org\/10.2178\/jsl\/1190150094","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2002,6]]}}}