دانلود کتاب سازگاری احتمالی جبری – بول، لوکاسیویچ، دی فینتی، کولموگروف

This book is primarily aimed at undergraduates in mathematics and computer science who wish to understand the symbiosis/equivalence between de Finetti’s finitely additive probability and Kolmogorov’s countably additive probability for continuous real-valued random variables on compact Hausdorff spaces. The book may also be of interest to philosophy students interested in the mutual relationship between consistency in logic and in probability, and to researchers interested in the algebraic approach to probability. The attraction force that determines the symbiosis between finitely additive and countably additive probability is given by de Finetti’s definition of a consistent [0, 1]-valued map on a finite set of {0, 1}-valued events. This is a generalization of a logically consistent assignment of truth-values in {0, 1} to a finite set of premises. The main application of this equivalence is the decidability of the consistency of a rational-valued assignment of probabilities to a finite set of continuous [0, 1]-valued events conditioned by another finite set of events. This is made possible by the deductive-algorithmic machinery of Łukasiewicz infinite-valued logic Ł∞, whose formulas code [0, 1]-valued events just as boolean formulas code {0, 1}-valued events. The key role of Ł∞-formulas is a consequence of the fundamental fact that Ł∞ is the unique logic generated by a continuous [0, 1]-valued operation satisfying the two minimalist conditions of what is commonly understood as an implication. Last, but not least, a notable feature of the equivalence between finitely additive and countably additive probability proved in this book is that logic and algebra play first violin in the symphony of mathematical results culminating in the proof of the equivalence. All these results will be the described in the final part of this introduction.