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 Logic and Conditional Probability
A Synthesis
Philip Calabrese
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 2valued statements to a 3valued 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
Nontrivially 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 realvalued functions with possibly different or overlapping domains of definition
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
25 October 2017
9781848902589
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