Logic and Conditional Probability

This monograph develops an algebra of Boolean fractions, (ab) - orderedpairs of propositions or events - "a if b," "event a given event b." In ninechapters, the author shows that these conditional propositions (together withtheir associated instantiations or models): Provide logical elements that be [...]
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This monograph develops an algebra of Boolean fractions, (ab) - orderedpairs of propositions or events - "a if b," "event a given event b." In ninechapters, the author shows that these conditional propositions (together withtheir associated instantiations or models): Provide logical elements that better represent and more faithfully facilitatemanipulation of certain and uncertain conditional informationExtend the Boole's algebra of 2-valued statements to a 3-valued systemthat includes "inapplicable statements" - those whose condition may befalse in some or all instances (examples, cases, models...)Allow a definition of the probability of an arbitrary Boolean propositionNon-trivially combine Boolean logic with standard conditional probabilitytheoryProvide a complete and adequate development of the crucial 4th operationfor Boolean logic, namely conditioning, including iterated conditioningProvide an expanded theory of deduction defined in terms of the extendedoperations on the Boolean fractionsAdmit a variety of deduction relations, and that the deductively closed setsgenerated by some initial set of conditionals can be calculatedExtend the ordinary function operations of sum, difference, product "ient to real-valued functions with possibly different or overlappingdomains of definitionRepresent & simplify complex conditional statements in Bayesian expertsystems used to calculate maximum information entropy solutionsExplicate the logic of quantum measurements by better expressing thechanging conditions in quantum mechanics