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Lukasiewicz's Logics and Prime Numbers
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.
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Lukasiewicz's Logics and Prime Numbers
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.
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Lukasiewicz's Logics and Prime Numbers

Lukasiewicz's Logics and Prime Numbers

by Alexander S Karpenko
Lukasiewicz's Logics and Prime Numbers

Lukasiewicz's Logics and Prime Numbers

by Alexander S Karpenko

Overview

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.

Product Details

ISBN-13: 9780955117039
Publisher: Luniver Press
Publication date: 01/01/2006
Pages: 168
Sales rank: 966,056
Product dimensions: 6.00(w) x 9.00(h) x 0.39(d)
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