{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,28]],"date-time":"2025-10-28T00:26:46Z","timestamp":1761611206114},"reference-count":20,"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 prove a representation theorem for (abstract) residuated algebras: each residuated algebra is isomorphically embeddable into a powerset residuated algebra. As a consequence, we obtain a completeness theorem for the Generalized Lambek Calculus. We use a Labelled Deductive System which generalizes the one used by Buszkowski [4] and Pankrat'ev [17] in completeness theorems for the Lambek Calculus.<\/jats:p>","DOI":"10.1002\/malq.19970430108","type":"journal-article","created":{"date-parts":[[2007,5,30]],"date-time":"2007-05-30T15:24:45Z","timestamp":1180538685000},"page":"60-72","source":"Crossref","is-referenced-by-count":12,"title":["Powerset Residuated Algebras and Generalized Lambek Calculus"],"prefix":"10.1002","volume":"43","author":[{"given":"Miroslawa","family":"Kolowska\u2010Gawiejnowicz","sequence":"first","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2006,11,13]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01066355"},{"key":"e_1_2_1_3_2","volume-title":"Language in Action: Categories, Lambdas and Dynamic Logic","author":"van Benthem J.","year":"1991"},{"key":"e_1_2_1_4_2","first-page":"57","volume-title":"Frege Conference 1984","author":"Buszkowski W.","year":"1984"},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.1002\/malq.19860320104"},{"key":"e_1_2_1_6_2","volume-title":"Logical Foundations of Ajdukiewicz\u2010Lambek Categorial Grammars","author":"Buszkowski W.","year":"1989"},{"key":"e_1_2_1_7_2","doi-asserted-by":"crossref","DOI":"10.1075\/llsee.25","volume-title":"Categorial Grammar","author":"Buszkowski W.","year":"1988"},{"key":"e_1_2_1_8_2","volume-title":"Substructural Logics","author":"Do\u0161en K.","year":"1993"},{"key":"e_1_2_1_9_2","doi-asserted-by":"crossref","unstructured":"Dunn J. 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