Some lattice models of bilinear logic
type: Item
instance of: scholarly article
title: Some lattice models of bilinear logic
zbMATH Open document ID: 0840.03044
DOI: 10.1007/BF01181877
published in: Algebra Universalis
publication date: 1996-01-23T00:00:00Z
review text: Bilinear logic is treated in the paper as a logic without the three Gentzen structural rules: interchange, weakening and contraction. It is a non-commutative version of linear logic which allows two negations. Only classical propositional bilinear logic is actually considered. The author aims at presenting the class of Grishin algebras, generalizations of Boolean algebras that serve as models of bilinear logic. A Grishin algebra is essentially a residuated lattice-ordered monoid with two additional unary operations (negations). Some elementary properties of Grishin algebras are described. In particular, the lattice \(L(G)\) of downward closed subsets of a Grishin algebra \(G\) is again a Grishin algebra. It is shown that if \(G\) has certain special properties, then the two negation operations on \(L(G)\) are distinct.
reviewed by: Jānis Cīrulis
Mathematics Subject Classification ID: 03G10
Mathematics Subject Classification ID: 03B20
zbMATH DE Number: 836833
zbMATH Keywords: bilinear logic
zbMATH Keywords: Grishin algebras
zbMATH Keywords: residuated lattice-ordered monoid
MaRDI profile type: Publication
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author: J. Lambek
description: scientific article; zbMATH DE number 836833