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Residuated Lattices An Algebraic Glimpse At Substructural Logics

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Residuated Lattices An Algebraic Glimpse at Substructural Logics

Residuated Lattices  An Algebraic Glimpse at Substructural Logics Book
Author : Nikolaos Galatos,Peter Jipsen,Tomasz Kowalski,Hiroakira Ono
Publisher : Elsevier
Release : 2007-04-25
ISBN : 9780080489643
Language : En, Es, Fr & De

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Book 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 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.

Interval Probabilistic Uncertainty and Non classical Logics

Interval   Probabilistic Uncertainty and Non classical Logics Book
Author : Van-Nam Huynh,Yoshiteru Nakamori,Hiroakira Ono,Jonathan Lawry,Vladik Kreinovich,Hung T. Nguyen
Publisher : Springer Science & Business Media
Release : 2008-01-11
ISBN : 9783540776642
Language : En, Es, Fr & De

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Book Description :

This book contains the proceedings of the first International Workshop on Interval/Probabilistic Uncertainty and Non Classical Logics, Ishikawa, Japan, March 25-28, 2008. The workshop brought together researchers working on interval and probabilistic uncertainty and on non-classical logics. It is hoped this workshop will lead to a boost in the much-needed collaboration between the uncertainty analysis and non-classical logic communities, and thus, to better processing of uncertainty.

Trends in Logic

Trends in Logic Book
Author : Vincent F. Hendricks,Jacek Malinowski
Publisher : Springer Science & Business Media
Release : 2013-03-09
ISBN : 9401735980
Language : En, Es, Fr & De

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Book Description :

In 1953, exactly 50 years ago to this day, the first volume of Studia Logica appeared under the auspices of The Philosophical Committee of The Polish Academy of Sciences. Now, five decades later the present volume is dedicated to a celebration of this 50th Anniversary of Studia Logica. The volume features a series of papers by distinguished scholars reflecting both the aim and scope of this journal for symbolic logic.

The Application of Fuzzy Logic for Managerial Decision Making Processes

The Application of Fuzzy Logic for Managerial Decision Making Processes Book
Author : Andreas Meier,Edy Portmann,Kilian Stoffel,Luis Terán
Publisher : Springer
Release : 2017-03-30
ISBN : 3319540483
Language : En, Es, Fr & De

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Book Description :

This book addresses the latest research and applications of fuzzy management methods for business decisions. It showcases a broad set of applications and discusses topics such as measures for the quality of analytics outcomes in big data environments; how fuzzy management methods support the inclusion of human thinking and human behavior in decision making processes; how to generate better results with fuzzy management methods in cases of imprecise information; new personalization concepts enabled by fuzzy logic for the offering of customized products and services especially in the electronic market; and lastly the application of fuzzy analysis for executives using natural rather than computer language. The combination of research papers and case studies makes it a valuable resource both for researchers and practitioners in the digital economy.

Non commutative Multiple Valued Logic Algebras

Non commutative Multiple Valued Logic Algebras Book
Author : Lavinia Corina Ciungu
Publisher : Springer Science & Business Media
Release : 2013-08-23
ISBN : 3319015893
Language : En, Es, Fr & De

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Book Description :

This monograph provides a self-contained and easy-to-read introduction to non-commutative multiple-valued logic algebras; a subject which has attracted much interest in the past few years because of its impact on information science, artificial intelligence and other subjects. A study of the newest results in the field, the monograph includes treatment of pseudo-BCK algebras, pseudo-hoops, residuated lattices, bounded divisible residuated lattices, pseudo-MTL algebras, pseudo-BL algebras and pseudo-MV algebras. It provides a fresh perspective on new trends in logic and algebras in that algebraic structures can be developed into fuzzy logics which connect quantum mechanics, mathematical logic, probability theory, algebra and soft computing. Written in a clear, concise and direct manner, Non-Commutative Multiple-Valued Logic Algebras will be of interest to masters and PhD students, as well as researchers in mathematical logic and theoretical computer science.

Manuscrito

Manuscrito Book
Author : N.A
Publisher :
Release : 2011
ISBN :
Language : En, Es, Fr & De

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LogKCA 07

LogKCA 07 Book
Author : N.A
Publisher : Universidad del Pais Basco Servicio Editorial
Release : 2007
ISBN :
Language : En, Es, Fr & De

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Actas

Actas Book
Author : N.A
Publisher :
Release : 2007
ISBN :
Language : En, Es, Fr & De

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Book Description :