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Algebraic Probabilistic Consistency: Boole, Łukasiewicz, de Finetti, Kolmogorov

By (author) Daniele Mundici





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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.

| product details |



Normally shipped | Enquiries only
Publisher | Springer International Publishing AG
Published date | 13 Sep 2025
Language |
Format | Hardback
Pages | 144
Dimensions | 235 x 155 x 0mm (L x W x H)
Weight | 0g
ISBN | 978-3-0319-8336-8
Readership Age |
BISAC | philosophy / logic

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