New foundations of information theory : logical entropy and Shannon entropy / / David Ellerman

• Autore: Ellerman David P.
• Pubblicazione: Cham, Switzerland : , : Springer, , [2021]; ©2021
• Descrizione fisica: 1 online resource (121 pages)
• Disciplina: 003.54
• Soggetto topico: Entropy (Information theory); Entropia (Teoria de la informació)
• Soggetto genere / forma: Llibres electrònics
• Nota di contenuto: Intro -- Acknowledgements -- About this book -- Contents -- About the Author -- 1 Logical Entropy -- 1.1 Introduction -- 1.2 Logical Information as the Measure of Distinctions -- 1.3 Classical Logical Probability and Logical Entropy -- 1.4 Information Algebras and Joint Distributions -- 1.5 Brief History of the Logical Entropy Formula -- References -- 2 The Relationship Between Logical Entropy and Shannon Entropy -- 2.1 Shannon Entropy -- 2.2 Logical Entropy, Not Shannon Entropy, Is a (Non-negative) Measure -- 2.3 The Dit-Bit Transform -- References -- 3 The Compound Notions for Logical and Shannon Entropies -- 3.1 Conditional Logical Entropy -- 3.2 Shannon Conditional Entropy -- 3.3 Logical Mutual Information -- 3.4 Shannon Mutual Information -- 3.5 Independent Joint Distributions -- 3.6 Cross-Entropies, Divergences, and Hamming Distance -- 3.6.1 Cross-Entropies -- 3.6.2 Divergences -- 3.6.3 Hamming Distance -- 3.7 Summary of Formulas and Dit-Bit Transforms -- References -- 4 Further Developments of Logical Entropy -- 4.1 Entropies for Multivariate Joint Distributions -- 4.2 An Example of Negative Mutual Information for Shannon Entropy -- 4.3 Entropies for Countable Probability Distributions -- 4.4 Metrical Logical Entropy = (Twice) Variance -- 4.5 Boltzmann and Shannon Entropies: A Conceptual Connection? -- 4.6 MaxEntropies for Discrete Distributions -- 4.7 The Transition to Coding Theory -- 4.8 Logical Entropy on Rooted Trees -- References -- 5 Quantum Logical Information Theory -- 5.1 Density Matrix Treatment of Logical Entropy -- 5.2 Linearizing Logical Entropy to Quantum Logical Entropy -- 5.3 Theorems About Quantum Logical Entropy -- 5.4 Quantum Logical Entropies with Density Matrices as Observables -- 5.5 The Logical Hamming Distance Between Two Partitions -- 5.6 The Quantum Logical Hamming Distance -- References -- 6 Conclusion. ; 6.1 Information Theory Re-founded and Re-envisioned -- 6.2 Quantum Information Theory Re-envisioned -- 6.3 What Is to Be Done? -- References -- A Basics of Partition Logic -- A.1 Subset Logic and Partition Logic -- A.2 The Lattice Operations on Partitions -- A.3 Implication and Negation in Partition Logic -- A.4 Relative Negation in Partition Logic and the Boolean Core -- A.5 Partition Tautologies -- References -- Index.
• Titolo autorizzato: New foundations of information theory
• ISBN: 3-030-86552-5
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 996466407803316
• Lo trovi qui: Univ. di Salerno
• Serie: SpringerBriefs in philosophy.