Residuated Lattices: An Algebraic Glimpse at Substructural Logics
：An Algebraic Glimpse at Substructural Logics
( Volume 151 )
Publication subTitle ：An Algebraic Glimpse at Substructural Logics
Publication series ：Volume 151
Author： Galatos Nikolaos;Jipsen Peter;Kowalski Tomasz
Publisher： Elsevier Science
Publication year： 2007
E-ISBN: 9780080489643
P-ISBN(Paperback): 9780444521415
P-ISBN(Hardback): 9780444521415
Subject： O1 Mathematics;O15 algebra, number theory, combinatorial theory;O158 Discrete Mathematics;TP3 Computers
Language： ENG
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Description
The book is meant to serve two purposes. The first and more obvious one is to present state of the art results in algebraic research into residuated structures related to substructural logics. The second, less obvious but equally important, is to provide a reasonably gentle introduction to algebraic logic. At the beginning, the second objective is predominant. Thus, in the first few chapters the reader will find a primer of universal algebra for logicians, a crash course in nonclassical logics for algebraists, an introduction to residuated structures, an outline of Gentzen-style calculi as well as some titbits of proof theory - the celebrated Hauptsatz, or cut elimination theorem, among them. These lead naturally to a discussion of interconnections between logic and algebra, where we try to demonstrate how they form two sides of the same coin. We envisage that the initial chapters could be used as a textbook for a graduate course, perhaps entitled Algebra and Substructural Logics.
As the book progresses the first objective gains predominance over the second. Although the precise point of equilibrium would be difficult to specify, it is safe to say that we enter the technical part with the discussion of various completions of residuated structures. These include Dedekind-McNeille completions and canonical extensions. Completions are used later in investigating several finiteness properties such as the finite model property, generation of varieties by their finite mem
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