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Powerset Residuated Algebras and Generalized Lambek Calculus
Author(s) -
KolowskaGawiejnowicz Miroslawa
Publication year - 1997
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.19970430108
Subject(s) - mathematics , completeness (order theory) , calculus (dental) , representation (politics) , algebra over a field , residuated lattice , representation theorem , pure mathematics , fuzzy logic , computer science , artificial intelligence , mathematical analysis , medicine , dentistry , politics , political science , law
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.