Neutrality and Many-Valued Logics

Neutrality and Many-Valued Logics
Author :
Publisher : Infinite Study
Total Pages : 123
Release :
ISBN-10 : 9781599730264
ISBN-13 : 159973026X
Rating : 4/5 (26X Downloads)

Book Synopsis Neutrality and Many-Valued Logics by : Andrew Schumann

Download or read book Neutrality and Many-Valued Logics written by Andrew Schumann and published by Infinite Study. This book was released on 2007 with total page 123 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, we consider various many-valued logics: standard, linear, hyperbolic, parabolic, non-Archimedean, p-adic, interval, neutrosophic, etc. We survey also results which show the tree different proof-theoretic frameworks for many-valued logics, e.g. frameworks of the following deductive calculi: Hilbert's style, sequent, and hypersequent. Recall that hypersequents are a natural generalization of Gentzen's style sequents that was introduced independently by Avron and Pottinger. In particular, we consider Hilbert's style, sequent, and hypersequent calculi for infinite-valued logics based on the three fundamental continuous t-norms: Lukasiewicz's, Godel?s, and Product logics. We present a general way that allows to construct systematically analytic calculi for a large family of non-Archimedean many-valued logics: hyperrational-valued, hyperreal-valued, and p-adic valued logics characterized by a special format of semantics with an appropriate rejection of Archimedes' axiom. These logics are built as different extensions of standard many-valued logics (namely, Lukasiewicz's, Godel?s, Product, and Post's logics). The informal sense of Archimedes' axiom is that anything can be measured by a ruler. Also logical multiple-validity without Archimedes' axiom consists in that the set of truth values is infinite and it is not well-founded and well-ordered. We consider two cases of non-Archimedean multi-valued logics: the first with many-validity in the interval [0,1] of hypernumbers and the second with many-validity in the ring of p-adic integers. Notice that in the second case we set discrete infinite-valued logics. Logics investigated: 1. hyperrational valued Lukasiewicz's, Godel?s, and Product logics, 2. hyperreal valued Lukasiewicz's, Godel?s, and Product logics, 3. p-adic valued Lukasiewicz's, Godel?s, and Post's logics.


Neutrality and Many-Valued Logics Related Books

Neutrality and Many-Valued Logics
Language: en
Pages: 123
Authors: Andrew Schumann
Categories: Mathematics
Type: BOOK - Published: 2007 - Publisher: Infinite Study

DOWNLOAD EBOOK

In this book, we consider various many-valued logics: standard, linear, hyperbolic, parabolic, non-Archimedean, p-adic, interval, neutrosophic, etc. We survey a
The Many Valued and Nonmonotonic Turn in Logic
Language: en
Pages: 691
Authors: Dov M. Gabbay
Categories: Mathematics
Type: BOOK - Published: 2007-08-13 - Publisher: Elsevier

DOWNLOAD EBOOK

The present volume of the Handbook of the History of Logic brings together two of the most important developments in 20th century non-classical logic. These are
Topics in Philosophical Logic
Language: en
Pages: 360
Authors: N. Rescher
Categories: Philosophy
Type: BOOK - Published: 2013-03-09 - Publisher: Springer Science & Business Media

DOWNLOAD EBOOK

The aim of the book is to introduce the reader to some new areas oflogic which have yet to find their way into the bulk of modern logic books written from the m
Computer Science and Multiple-Valued Logic
Language: en
Pages: 563
Authors: David C. Rine
Categories: Technology & Engineering
Type: BOOK - Published: 2014-05-12 - Publisher: Elsevier

DOWNLOAD EBOOK

Computer Science and Multiple-Valued Logic: Theory and Applications focuses on the processes, methodologies, and approaches involved in multiple-valued logic an
Neutrosophic logics on Non-Archimedean Structures
Language: en
Pages: 23
Authors: Andrew Schumann
Categories: Mathematics
Type: BOOK - Published: - Publisher: Infinite Study

DOWNLOAD EBOOK

We present a general way that allows to construct systematically analytic calculi for a large family of non-Archimedean many-valued logics: hyperrational-valued