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Neutrality and Many-Valued Logics

By Schumann, Andrew

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Book Id: WPLBN0100302889
Format Type: PDF (eBook)
File Size: 798.00 KB.
Reproduction Date: 11/1/2007

Title: Neutrality and Many-Valued Logics  
Author: Schumann, Andrew
Language: English
Subject: Non Fiction, Philosophy
Collections: Philosophy, Authors Community
Publication Date:
Publisher: American Research Press
Member Page: Infinite Science


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Schumann, A., & Smarandache, F. (2007). Neutrality and Many-Valued Logics. Retrieved from

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.


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