Powerset Residuated Algebras and Generalized Lambek Calculus | Zendy

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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.

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