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The Structural Theory of Probability Paolo Rocchi

The Structural Theory of Probability By Paolo Rocchi

The Structural Theory of Probability by Paolo Rocchi

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Summary

Dr. Rocchi's topical and ever-timely volume proposes a novel, exhaustive solution to this vibrant issue.

Paolo Rocchi, a versatile IBM scientist, outlines a new philosophical and mathematical approach inspired by well-tested software techniques.

The Structural Theory of Probability Summary

The Structural Theory of Probability: New Ideas from Computer Science on the Ancient Problem of Probability Interpretation by Paolo Rocchi

The Structural Theory of Probability addresses the interpretation of probability, often debated in the scientific community. This problem has been examined for centuries; perhaps no other mathematical calculation suffuses mankind's efforts at survival as amply as probability. In the dawn of the 20th century David Hilbert included the foundations of the probability calculus within the most vital mathematical problems; Dr. Rocchi's topical and ever-timely volume proposes a novel, exhaustive solution to this vibrant issue.

Paolo Rocchi, a versatile IBM scientist, outlines a new philosophical and mathematical approach inspired by well-tested software techniques. Through the prism of computer technology he provides an innovative view on the theory of probability. Dr. Rocchi discusses in detail the mathematical tools used to clarify the meaning of probability, integrating with care numerous examples and case studies. The comprehensiveness and originality of its mathematical development make this volume an inspiring read for researchers and students alike.

The Structural Theory of Probability Reviews

From the reviews:

"The structural theory of probability addresses the interpretation of probability, often debated in the scientific community. Rocchis topical and ever-timely volume proposes a novel, exhaustive solution to this vibrant issue." (Rainer Beedgen, Zentralblatt MATH, Vol. 1069 (20), 2005)

"Probability theory from Pascal to Kolmogorov has focused on the events as sets of outcomes or results, and probablity as a measure attached to these sets. But this ignores the structure of the processes which lead to the outcomes, and the author explores how taking into account the details of the process would lead to a more fundamental understanding of the nature of probability. ... One hopes that in due course the author will develop his theories further and present overwhelmingly persuasive examples of the advantages of his approach." ---MAA reviews

Table of Contents

1 Cultural Roots.- 1.1 Operational analysis.- 1.2 Networks.- 1.3 Innovative improvements.- 2 Critical Remarks.- 2.1 Random events overlooked.- 2.2 Ensemble model.- 2.3 Linguistic model.- 2.4 Which is the probability argument?.- 2.5 A new proposal.- 3 Events and Structures.- 3.1 Connecting is primitive.- 3.2 Entities, relationships and structures.- 3.3 Abstract algebra.- 3.4 Structural model.- 3.5 Structures advantages.- 3.6 Successful structures.- 4 Notes on Structural Analysis.- 4.1 Main mechanisms in events.- 4.2 Basic structural forms.- 4.3 Three singular cases.- 4.4 Why they do not have a general application.- 5 Certainty and Uncertainty.- 5.1 Difficulties in investigating the reality.- 5.2 Uncertain details.- 5.3 Structure of levels.- 5.4 What the levels make explicit.- 5.5 Certain and uncertain structures.- 5.6 Uncertainty and randomness.- 5.7 Progressive qualities of knowledge.- 6 Probability.- 6.1 The problem of being.- 6.2 Definition of probability.- 6.3 Advantages from the definition.- 7 Relative Frequency.- 7.1 Rounding.- 7.2 Experimental test.- 7.3 Frequency and probability are identical.- 7.4 Frequency and probability do not coincide.- 7.5 The Law of large numbers.- 7.6 Practical applications of the law.- 8 Objectivism and Subjectivism.- 8.1 The meaning of probability.- 8.2 Theoretical schools.- 8.3 Theory and praxis.- 8.4 Science of indeterminism.- 9 Probability Calculus.- 9.1 The Laplace formula.- 9.2 Function of probability.- 9.3 Theorem of compound probabilities.- 9.4 Theorem of total probabilities.- 9.5 Closing remarks.- 10 Conditional Probability.- 10.1 Effects from causes.- 10.2 Dependence and independence.- 10.3 Probability of the third singular case.- 10.4 The Bayes theorem.- 11 Stochastic Systems.- 11.1 Transition matrix.- 11.2Chapman-Kolmogorovs theorem.- 11.3 State matrix.- 11.4 Evolution theorem.- 12 Distributions.- 12.1 Distribution functions.- 12.2 Constant distribution.- 12.3 Binomial distribution.- 12.4 Poissons distribution.- 12.5 Normal distribution.- 12.6 Compound distributions.- 13 Bivalent and Multivalent Logic.- 13.1 Probability and language.- 13.2 Values of truth and probability.- 13.3 Logic calculus.- 14 Two Applications.- 14.1 Exercise I.- 14.2 Exercise II.- Appendix: Historys Lessons.- 1 Classical culture.- 2 The rule of apodictic reasoning.- 3 Uncertainty appears in jurisprudence.- 4 People begin to calculate chances.- 5 Statistics emerges.- 6 Two veins merge.- 7 Toward a systematic study.- 8 Several fields are invaded.- 9 Multivalent logic.- 10 The fundamentals are still obscure.- Index of Subjects.- Index of Names.

Additional information

NPB9780306474286
9780306474286
030647428X
The Structural Theory of Probability: New Ideas from Computer Science on the Ancient Problem of Probability Interpretation by Paolo Rocchi
Paolo Rocchi
Series in Computer Science
New
Hardback
Springer Science+Business Media
2003-01-31
162
N/A
Book picture is for illustrative purposes only, actual binding, cover or edition may vary.
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