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
An Introduction to Non-Classical Logic
Language: en
Pages: 582
Authors: Graham Priest
Categories: Science
Type: BOOK - Published: 2008-04-10 - Publisher: Cambridge University Press

DOWNLOAD EBOOK

This revised and considerably expanded 2nd edition brings together a wide range of topics, including modal, tense, conditional, intuitionist, many-valued, parac
Many-Valued Logics 1
Language: en
Pages: 310
Authors: Leonard Bolc
Categories: Computers
Type: BOOK - Published: 1992-11-12 - Publisher: Springer Science & Business Media

DOWNLOAD EBOOK

Many-valued logics were developed as an attempt to handle philosophical doubts about the "law of the excluded middle" in classical logic. This discussion, which
Modern Uses of Multiple-Valued Logic
Language: en
Pages: 341
Authors: M. Dunn
Categories: Philosophy
Type: BOOK - Published: 2012-12-06 - Publisher: Springer Science & Business Media

DOWNLOAD EBOOK

This is a collection of invited papers from the 1975 International Sym posium on Multiple-valued Logic. Also included is an extensive bib liography of works in
Neutrosophic information in the framework of multivalued representation
Language: en
Pages: 10
Authors: Vasile Patrascu
Categories:
Type: BOOK - Published: - Publisher: Infinite Study

DOWNLOAD EBOOK

The paper presents some steps for multi-valued representation of neutrosophic information. These steps are provided in the framework of multivalued logics using