Neutrality and Many-Valued Logics

By Schumann, Andrew

Book Id: WPLBN0100302889
Format Type: PDF eBook:
File Size: 0.8 MB
Reproduction Date: 11/1/2007

Title:	Neutrality and Many-Valued Logics
Author:	Schumann, Andrew
Volume:
Language:	English
Subject:	Non Fiction, Philosophy
Collections:	Philosophy, Authors Community
Historic Publication Date:	2007
Publisher:	American Research Press

Member Page:	Infinite Science
Citation APA MLA Chicago Schumann, B. A., & Smarandache, F. (2007). Neutrality and Many-Valued Logics. Retrieved from http://gutenberg.cc/

Description
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: Łukasiewicz's, Gödel’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.