Lukasiewicz S Logics And Prime Numbers
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Lukasiewicz S Logics And Prime Numbers
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Author : A. S. Karpenko
language : en
Publisher: Luniver Press
Release Date : 2006
Lukasiewicz S Logics And Prime Numbers written by A. S. Karpenko and has been published by Luniver Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Mathematics categories.
Is there any link between the doctrine of logical fatalism and prime numbers? What do logic and prime numbers have in common? The book adopts truth-functional approach to examine functional properties of finite-valued Lukasiewicz logics Ln+1. Prime numbers are defined in algebraic-logical terms (Finn's theorem) and represented as rooted trees. The author designs an algorithm which for every prime number n constructs a rooted tree where nodes are natural numbers and n is a root. Finite-valued logics Kn+1 are specified that they have tautologies if and only if n is a prime number. It is discovered that Kn+1 have the same functional properties as Ln+1 whenever n is a prime number. Thus, Kn+1 are 'logics' of prime numbers. Amazingly, combination of logics of prime numbers led to uncovering a law of generation of classes of prime numbers. Along with characterization of prime numbers author also gives characterization, in terms of Lukasiewicz logical matrices, of powers of primes, odd numbers, and even numbers.
Neutrality And Many Valued Logics
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Author : Andrew Schumann
language : en
Publisher: Infinite Study
Release Date : 2007
Neutrality And Many Valued Logics written by Andrew Schumann and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.
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.
The History And Philosophy Of Polish Logic
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Author : K. Mulligan
language : en
Publisher: Springer
Release Date : 2016-01-26
The History And Philosophy Of Polish Logic written by K. Mulligan and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-01-26 with Philosophy categories.
The book presents the state of the art of research into the legacy of interwar Polish analytic philosophy and exemplifies different approaches to the history of philosophy. It contains discussions and reconstructions of aspects of Polish philosophy and logic as well as reactions to and developments of this tradition.
Initiatives In Logic
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Author : Jan J.T. Srzednicki
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Initiatives In Logic written by Jan J.T. Srzednicki and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Philosophy categories.
The Lvov Warsaw School Past And Present
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Author : Ángel Garrido
language : en
Publisher: Birkhäuser
Release Date : 2018-06-12
The Lvov Warsaw School Past And Present written by Ángel Garrido and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-06-12 with Mathematics categories.
This is a collection of new investigations and discoveries on the history of a great tradition, the Lvov-Warsaw School of logic and mathematics, by the best specialists from all over the world. The papers range from historical considerations to new philosophical, logical and mathematical developments of this impressive School, including applications to Computer Science, Mathematics, Metalogic, Scientific and Analytic Philosophy, Theory of Models and Linguistics.
Proof Theory And Algebra In Logic
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Author : Hiroakira Ono
language : en
Publisher: Springer
Release Date : 2019-08-02
Proof Theory And Algebra In Logic written by Hiroakira Ono and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-08-02 with Philosophy categories.
This book offers a concise introduction to both proof-theory and algebraic methods, the core of the syntactic and semantic study of logic respectively. The importance of combining these two has been increasingly recognized in recent years. It highlights the contrasts between the deep, concrete results using the former and the general, abstract ones using the latter. Covering modal logics, many-valued logics, superintuitionistic and substructural logics, together with their algebraic semantics, the book also provides an introduction to nonclassical logic for undergraduate or graduate level courses.The book is divided into two parts: Proof Theory in Part I and Algebra in Logic in Part II. Part I presents sequent systems and discusses cut elimination and its applications in detail. It also provides simplified proof of cut elimination, making the topic more accessible. The last chapter of Part I is devoted to clarification of the classes of logics that are discussed in the second part. Part II focuses on algebraic semantics for these logics. At the same time, it is a gentle introduction to the basics of algebraic logic and universal algebra with many examples of their applications in logic. Part II can be read independently of Part I, with only minimum knowledge required, and as such is suitable as a textbook for short introductory courses on algebra in logic.
Logic Semantics Metamathematics
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Author : Alfred Tarski
language : en
Publisher: Hackett Publishing
Release Date : 1983-01-01
Logic Semantics Metamathematics written by Alfred Tarski and has been published by Hackett Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983-01-01 with Philosophy categories.
Symbolic And Quantitative Approaches To Reasoning With Uncertainty
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Author : Lluis Godo
language : en
Publisher: Springer
Release Date : 2005-08-25
Symbolic And Quantitative Approaches To Reasoning With Uncertainty written by Lluis Godo and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-08-25 with Computers categories.
These are the proceedings of the 8th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty, ECSQARU 2005, held in Barcelona (Spain), July 6–8, 2005. The ECSQARU conferences are biennial and have become a major forum for advances in the theory and practice of r- soning under uncertainty. The ?rst ECSQARU conference was held in Marseille (1991), and after in Granada (1993), Fribourg (1995), Bonn (1997), London (1999), Toulouse (2001) and Aalborg (2003). The papers gathered in this volume were selected out of 130 submissions, after a strict review process by the members of the Program Committee, to be presented at ECSQARU 2005. In addition, the conference included invited lectures by three outstanding researchers in the area, Seraf ́ ?n Moral (Imprecise Probabilities), Rudolf Kruse (Graphical Models in Planning) and J ́ erˆ ome Lang (Social Choice). Moreover, the application of uncertainty models to real-world problems was addressed at ECSQARU 2005 by a special session devoted to s- cessful industrial applications, organized by Rudolf Kruse. Both invited lectures and papers of the special session contribute to this volume. On the whole, the programme of the conference provided a broad, rich and up-to-date perspective of the current high-level research in the area which is re?ected in the contents of this volume. IwouldliketowarmlythankthemembersoftheProgramCommitteeandthe additional referees for their valuable work, the invited speakers and the invited session organizer.
Handbook Of Philosophical Logic
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Author : Dov M. Gabbay
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-08-28
Handbook Of Philosophical Logic written by Dov M. Gabbay and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-08-28 with Mathematics categories.
The fourteenth volume of the Second Edition covers central topics in philosophical logic that have been studied for thousands of years, since Aristotle: Inconsistency, Causality, Conditionals, and Quantifiers. These topics are central in many applications of logic in central disciplines and this book is indispensable to any advanced student or researcher using logic in these areas. The chapters are comprehensive and written by major figures in the field.
Foundations Of Mathematical Logic
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Author : Haskell Brooks Curry
language : en
Publisher: Courier Corporation
Release Date : 1977-01-01
Foundations Of Mathematical Logic written by Haskell Brooks Curry and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 1977-01-01 with Mathematics categories.
Written by a pioneer of mathematical logic, this comprehensive graduate-level text explores the constructive theory of first-order predicate calculus. It covers formal methods — including algorithms and epitheory — and offers a brief treatment of Markov's approach to algorithms. It also explains elementary facts about lattices and similar algebraic systems. 1963 edition.