Algebraic Probabilistic Consistency
Boole, Łukasiewicz, de Finetti, Kolmogorov
Series: Trends in Logic; 69;
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Product details:
- Publisher Springer Nature Switzerland
- Date of Publication 16 November 2025
- Number of Volumes 1 pieces, Book
- ISBN 9783031983368
- Binding Hardback
- No. of pages144 pages
- Size 235x155 mm
- Language English
- Illustrations XVI, 144 p. 2 illus. Illustrations, black & white 700
Categories
Long description:
This book investigates the foundations of probability theory and logic, intertwining historical insights with modern interpretations. It explores the evolution of probability theory from Boole’s seminal question on the very object of probability, through de Finetti’s finitely additive probability and his consistency notion, also known as “non-Dutchbookability,” to the intricate relationship between logic independence and stochastic independence. Using the recent characterization of Łukasiewicz logic as the only logic generated by a continuous [0,1]-valued operation having the two minimal properties of what is commonly understood as an implication, the author extends the results of the first part of the book from yes-no events to continuous real-valued events. The book culminates with a detailed examination of the symbiosis between de Finetti’s finitely additive and Kolmogorov’s countably additive probability on compact spaces. By providing a rigorous and cohesive narrative, this book serves as an essential resource for scholars and students in mathematical logic eager to grasp the profound connections between logic, probability, and algebraic structures.
MoreTable of Contents:
Geometry of finite boolean algebras and their states.- De Finetti’s “Fundamental Theorem of Probability”.- De Finetti’s Consistency Theorem.- Boolean independence, consistency, and the product law.- Interlude: de Finetti’s exchangeability theorem.- The logic L∞ of continuous [0, 1] valued events.- MV algebraic probabilistic consistency.- The product law for continuous [0, 1] events.- Finite/countable additivity.
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