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
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
