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LEADER 00000cam a2200745Ia 4500 
001    ocn162130498 
003    OCoLC 
005    20160527040939.2 
006    m     o  d         
007    cr cn||||||||| 
008    070802s2007    ne a    ob    001 0 eng d 
016 7  013662080|2Uk 
019    155851146|a441806486|a648300233|a779920621 
020    9780444521415 
020    0444521410 
020    9780080489643|q(electronic bk.) 
020    0080489648|q(electronic bk.) 
035    (OCoLC)162130498|z(OCoLC)155851146|z(OCoLC)441806486
037    116820:116920|bElsevier Science & Technology|nhttp:// 
049    RIDW 
050  4 QA10|b.R47 2007eb 
072  7 QA|2lcco 
072  7 MAT|x016000|2bisacsh 
072  7 MAT|x018000|2bisacsh 
082 04 511.33|222 
090    QA10|b.R47 2007eb 
245 00 Residuated lattices :|ban algebraic glimpse at 
       substructural logics /|cNikolaos Galatos [and others]. 
250    1st ed. 
260    Amsterdam ;|aBoston :|bElsevier,|c2007. 
300    1 online resource (xxi, 509 pages) :|billustrations. 
336    text|btxt|2rdacontent 
337    computer|bc|2rdamedia 
338    online resource|bcr|2rdacarrier 
490 1  Studies in logic and the foundations of mathematics,|x0049
       -237X ;|vv. 151 
504    Includes bibliographical references (pages 479-495) and 
505 0  Contents -- List of Figures -- List of Tables -- 
       Introduction -- Chapter 1. Getting started -- Chapter 2. 
       Substructural logics and residuated lattices -- Chapter 3.
       Residuation and structure theory -- Chapter 4. 
       Decidability -- Chapter 5. Logical and algebraic 
       properties -- Chapter 6. completions and finite 
       embeddability -- Chapter 7. Algebraic aspects of cut 
       elimination -- Chapter 8. Glivenko theorems -- Chapter 9. 
       Lattices of logics and varieties -- Chapter 10. Splittings
       -- Chapter 11. Semisimplicity -- Bibliography -- Index. 
520    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 members, and finite embeddability. The 
       algebraic analysis of cut elimination that follows, also 
       takes recourse to completions. Decidability of logics, 
       equational and quasi-equational theories comes next, where
       we show how proof theoretical methods like cut elimination
       are preferable for small logics/theories, but semantic 
       tools like Rabin's theorem work better for big ones. Then 
       we turn to Glivenko's theorem, which says that a formula 
       is an intuitionistic tautology if and only if its double 
       negation is a classical one. We generalise it to the 
       substructural setting, identifying for each substructural 
       logic its Glivenko equivalence class with smallest and 
       largest element. This is also where we begin investigating
       lattices of logics and varieties, rather than particular 
       examples. We continue in this vein by presenting a number 
       of results concerning minimal varieties/maximal logics. A 
       typical theorem there says that for some given well-known 
       variety its subvariety lattice has precisely such-and-such
       number of minimal members (where values for such-and-such 
       include, but are not limited to, continuum, countably many
       and two). In the last two chapters we focus on the lattice
       of varieties corresponding to logics without contraction. 
       In one we prove a negative result: that there are no 
       nontrivial splittings in that variety. In the other, we 
       prove a positive one: that semisimple varieties coincide 
       with discriminator ones. Within the second, more technical
       part of the book another transition process may be traced.
       Namely, we begin with logically inclined technicalities 
       and end with algebraically inclined ones. Here, perhaps, 
       algebraic rendering of Glivenko theorems marks the 
       equilibrium point, at least in the sense that finiteness 
       properties, decidability and Glivenko theorems are of 
       clear interest to logicians, whereas semisimplicity and 
       discriminator varieties are universal algebra par 
       exellence. It is for the reader to judge whether we 
       succeeded in weaving these threads into a seamless fabric.
       - Considers both the algebraic and logical perspective 
       within a common framework. - Written by experts in the 
       area. - Easily accessible to graduate students and 
       researchers from other fields. - Results summarized in 
       tables and diagrams to provide an overview of the area. - 
       Useful as a textbook for a course in algebraic logic, with
       exercises and suggested research directions. - Provides a 
       concise introduction to the subject and leads directly to 
       research topics. - The ideas from algebra and logic are 
       developed hand-in-hand and the connections are shown in 
       every level. 
588 0  Print version record. 
590    eBooks on EBSCOhost|bEBSCO eBook Subscription Academic 
       Collection - North America 
650  0 Algebraic logic. 
650  0 Lattice theory. 
655  4 Electronic books. 
700 1  Galatos, Nikolaos. 
776 08 |iPrint version:|tResiduated lattices.|b1st ed.|dAmsterdam
       ; Boston : Elsevier, 2007|z9780444521415|z0444521410
830  0 Studies in logic and the foundations of mathematics ;|vv. 
856 40 |u
       db=nlebk&AN=196232|zOnline eBook. Access restricted to 
       current Rider University students, faculty, and staff. 
856 42 |3Instructions for reading/downloading this eBook|uhttp:// 
948    |d20160615|cEBSCO|tebscoebooksacademic|lridw 
994    92|bRID