Logic

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.