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This monograph develops an algebra of Boolean fractions, (ab) - ordered pairs of propositions or events - "a if b", "event a given event b". In nine chapters, the author shows that these conditional propositions (together with their associated instantiations or models):
Provide logical elements that better represent and more faithfully facilitate manipulation of certain and uncertain conditional information
Extend the Boole's algebra of 2-valued statements to a 3-valued system that includes "inapplicable statements" - those whose condition may be false in some or all instances (examples, cases, models...)
Allow a definition of the probability of an arbitrary Boolean proposition
Non-trivially combine Boolean logic with standard conditional probability theory
Provide a complete and adequate development of the crucial 4th operation for Boolean logic, namely conditioning, including iterated conditioning
Provide an expanded theory of deduction defined in terms of the extended operations on the Boolean fractions
Admit a variety of deduction relations, and that the deductively closed sets generated by some initial set of conditionals can be calculated
Extend the ordinary function operations of sum, difference, product & quotient to real-valued functions with possibly different or overlapping domains of definition
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Edition | Availability |
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1
Logic And Conditional Probability: A Synthesis
October 25, 2017, College Publications
Paperback
in English
- First edition
1848902581 9781848902589
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Edition Notes
Represent & simplify complex conditional statements in Bayesian expert systems used to calculate maximum information entropy solutions. Explicate the logic of quantum measurements by better expressing the changing conditions in quantum mechanics.
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- Created October 23, 2019
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October 23, 2019 | Edited by Kaustubh Chakraborty | Added new cover |
October 23, 2019 | Edited by Kaustubh Chakraborty | Added new book |
October 23, 2019 | Created by Kaustubh Chakraborty | Added new book. |