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Logic: Foundations, the P-vs-NP-Problem and Information-Theoretic Perspectives
Paperback
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ISBN10: 3819202560
ISBN13: 9783819202568
Publisher: Bod - Books on Demand
Published: Jul 17 2025
Pages: 158
Weight: 0.36
Height: 0.37 Width: 5.00 Depth: 8.00
Language: English
ISBN13: 9783819202568
Publisher: Bod - Books on Demand
Published: Jul 17 2025
Pages: 158
Weight: 0.36
Height: 0.37 Width: 5.00 Depth: 8.00
Language: English
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.
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