{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,29]],"date-time":"2022-03-29T12:21:58Z","timestamp":1648556518609},"reference-count":9,"publisher":"Cambridge University Press (CUP)","issue":"4","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":4484,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2001,12]]},"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":"10.2307\/2694964","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T18:06:22Z","timestamp":1146938782000},"page":"1597-1619","source":"Crossref","is-referenced-by-count":1,"title":["Monoid based semantics for linear formulas"],"prefix":"10.1017","volume":"66","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":"S0022481200010185_ref009","first-page":"41","author":"Yetter","year":"1990","journal-title":"Quantales and (non-commutative) linear logic,"},{"key":"S0022481200010185_ref007","doi-asserted-by":"publisher","DOI":"10.1090\/conm\/092\/1003210"},{"key":"S0022481200010185_ref002","unstructured":"De Paiva V. , Categorical proof theory and linear logic, can be found in http:\/\/www.cs.bham.ac.uk\/vdp."},{"key":"S0022481200010185_ref001","unstructured":"Ambler S. , First order linear logic in symmetric monoidal closed categories. Ph.D. thesis, University of Edinburgh, 1991."},{"key":"S0022481200010185_ref004","volume-title":"London mathematical society lecture notes series,","author":"Girard","year":"1995"},{"key":"S0022481200010185_ref003","first-page":"1","volume-title":"Theoretical Computer Science,","author":"Girard","year":"1987"},{"key":"S0022481200010185_ref005","first-page":"99","volume":"12","author":"Mulvey","year":"1986","journal-title":"and, Rendiconti del Circolo Matematico di Palermo. Ser II Supplemento,"},{"key":"S0022481200010185_ref008","volume-title":"CSLl lectures notes,","author":"Troelstra","year":"1992"},{"key":"S0022481200010185_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\/S0022481200010185","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,7]],"date-time":"2019-05-07T22:14:46Z","timestamp":1557267286000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200010185\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2001,12]]},"references-count":9,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2001,12]]}},"alternative-id":["S0022481200010185"],"URL":"https:\/\/doi.org\/10.2307\/2694964","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2001,12]]}}}