{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,28]],"date-time":"2023-10-28T11:15:56Z","timestamp":1698491756780},"reference-count":18,"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":3603,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematical Logic Qtrly"],"published-print":{"date-parts":[[1997,1]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We present a categorical\/denotational semantics for the Lambek Syntactic Calculus (LSC), indeed for a \u03bblD\u2010typed version Curry\u2010Howard isomorphic to it. The main novelty of our approach is an abstract noncommutative construction with right and left adjoints, called sequential product. It is defined through a hierarchical structure of categories reflecting the implicit permission to sequence expressions and the inductive construction of compound expressions. We claim that Lambek's noncommutative product corresponds to a noncommutative bi\u2010endofunctor into a category, which encloses all categories of such hierarchical structure. A soundness theorem for LSC is shown with respect to this semantical framework.<\/jats:p>","DOI":"10.1002\/malq.19970430107","type":"journal-article","created":{"date-parts":[[2007,5,30]],"date-time":"2007-05-30T15:24:48Z","timestamp":1180538688000},"page":"49-59","source":"Crossref","is-referenced-by-count":1,"title":["A Concrete Categorical Model for the Lambek Syntactic Calculus"],"prefix":"10.1002","volume":"43","author":[{"given":"Marcelo","family":"Da Silva Corr\u00eaa","sequence":"first","affiliation":[]},{"given":"Edward Hermann","family":"Haeusler","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2006,11,13]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1002\/malq.19900360103"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1002\/malq.19860320104"},{"key":"e_1_2_1_4_2","unstructured":"Corr\u00eaa M. da S. andE. H.Haeusler A concrete categorical model for the Lambek calculus. Preliminary Report. Technical Report PUC\u2010RioInf. MCC24\/95 Dept. de Inform\u00e1tica Pontif\u00edcia Univ. Cat\u00f3lica PUC\u2010Rio July 1995. (An electronic copy is available atftp:\/\/ftp.inf.puc\u2010rio.br\/pub\/docs\/techreports\/95_24_correa.ps.gz)"},{"key":"e_1_2_1_5_2","volume-title":"A Dialectica Model of the Lambek Calculus","author":"De Paiva V. C. V.","year":"1991"},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.1002\/malq.19850311405"},{"key":"e_1_2_1_7_2","volume-title":"Proofs and Types","author":"Girard J.\u2010Y.","year":"1989"},{"key":"e_1_2_1_8_2","volume-title":"Topoi: The Categorical Analysis of Logic","author":"Goldblatt R.","year":"1979"},{"key":"e_1_2_1_9_2","first-page":"479","volume-title":"To H. B. Curry: Essays on Combinatory Logic, Lambda Calculus and Formalism","author":"Howard W. A.","year":"1980"},{"key":"e_1_2_1_10_2","doi-asserted-by":"publisher","DOI":"10.2307\/2310058"},{"key":"e_1_2_1_11_2","doi-asserted-by":"publisher","DOI":"10.1090\/psapm\/012\/9972"},{"key":"e_1_2_1_12_2","first-page":"278","article-title":"Deductive systems and categories I: Syntactic calculus and residuated categories","volume":"2","author":"Lambek J.","year":"1968","journal-title":"Math. Systems Theory"},{"key":"e_1_2_1_13_2","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0079385"},{"key":"e_1_2_1_14_2","doi-asserted-by":"publisher","DOI":"10.1090\/conm\/092\/1003201"},{"key":"e_1_2_1_15_2","first-page":"207","volume-title":"Substructural Logics","author":"Lambek J.","year":"1995"},{"key":"e_1_2_1_16_2","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511629150.003"},{"key":"e_1_2_1_17_2","volume-title":"Categories for the Working Mathematician","author":"Maclane S.","year":"1971"},{"key":"e_1_2_1_18_2","volume-title":"Natural Deduction: A Proof\u2010theoretical Study","author":"Prawitz D.","year":"1965"},{"key":"e_1_2_1_19_2","doi-asserted-by":"publisher","DOI":"10.2307\/2274953"}],"container-title":["Mathematical Logic Quarterly"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fmalq.19970430107","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/malq.19970430107","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,28]],"date-time":"2023-10-28T10:38:41Z","timestamp":1698489521000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/malq.19970430107"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1997,1]]},"references-count":18,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1997,1]]}},"alternative-id":["10.1002\/malq.19970430107"],"URL":"https:\/\/doi.org\/10.1002\/malq.19970430107","archive":["Portico"],"relation":{},"ISSN":["0942-5616","1521-3870"],"issn-type":[{"value":"0942-5616","type":"print"},{"value":"1521-3870","type":"electronic"}],"subject":[],"published":{"date-parts":[[1997,1]]}}}