Logic: Foundations, the P-vs-NP-Problem and Information-Theoretic Perspectives

Sina, Lucien

ISBN 10: 3819202560 / ISBN 13: 9783819202568

Published by Bod - Books on Demand, 2025

About this Item

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Seller Inventory # 408332596

Bibliographic Details

• Title: Logic: Foundations, the P-vs-NP-Problem and Information-Theoretic Perspectives
• Publisher: Bod - Books on Demand
• Publication Date: 2025
• Language: English
• ISBN 10: 3819202560
• ISBN 13: 9783819202568
• Binding: Soft cover
• Condition: New

About this title

Synopsis

This groundbreaking textbook presents a new approach to the study of logic by combining classical foundations with modern information-theoretic perspectives. Following a detailed introduction, it offers an information-theoretic formalization of logic. Subsequently, well-known but still unsolved problems, such as the P versus NP problem, are addressed using the provided tools. An optimization algorithm for the target requirements of logical problem-solving-regarding computability, expressiveness, and consistency-is presented, and finally, a few applications in other fields are showcased. The book offers students and researchers a comprehensive journey through the fundamental principles of logic while introducing innovative concepts at the intersection of logic, information theory, and computational complexity. Key features include: -Solid foundations in classical logic, including propositional and predicate logic, validity, and formal inference. -Novel integration of Shannon's information theory with traditional logical concepts. -Exploration of new approaches to axiomatization and formalization in light of Gödel's incompleteness results. -In-depth analysis of the P versus NP problem with information-theoretic and optimization approaches. -Clear explanations and examples suitable for beginners and beyond. -Applications in mathematics, computer science, and related fields.