Logic: Foundations, the P-vs-NP-Problem and Information-Theoretic Perspectives
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Beschreibung
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.
New approach to the study of logic
Information-theoretic formalization of logic
This book is intended for students, researchers, and anyone with a keen interest in the foundations of mathematics, logic, and theoretical computer science.
Autor*in
Lucien Sina
Lucien Sina is an experienced computer scientist and educator with a passion for making complex topics accessible. He has years of experience in developing and analyzing algorithms and guides readers through the essential concepts of computer science.
Themen in »Logic: Foundations, the P-vs-NP-Problem and Information-Theoretic Perspectives«
logic formal logic mathematics Computer Science Foundations of mathematics