Logic and Conditional Probability

<p>This monograph develops an algebra of Boolean <em>fractions</em>, (a|b) &ndash; ordered</p><p>pairs of propositions or events &ndash; &ldquo;a&nbsp;<em>if b</em>&rdquo;, &ldquo;event a <em>given </em>event b&rdquo;. In nine</p><p>chapters, the author shows that these conditional propositions (together with</p><p>their associated instantiations or models):</p><p>Provide logical elements that better represent and more faithfully facilitate</p><p>manipulation of certain and uncertain <em>conditional </em>information</p><p>Extend the Boole&rsquo;s algebra of 2-valued statements to a 3-valued system</p><p>that includes &ldquo;<em>inapplicable </em>statements&rdquo; - those whose condition may be</p><p>false in some or all instances (examples, cases, models...)</p><p>Allow a <em>definition </em>of the probability of an arbitrary Boolean proposition</p><p>Non-trivially combine Boolean logic with standard conditional probability</p><p>theory</p><p>Provide a complete and adequate development of the crucial 4th operation</p><p>for Boolean logic, namely <em>conditioning, </em>including iterated conditioning</p><p>Provide an expanded theory of deduction defined in terms of the extended</p><p>operations on the Boolean fractions</p><p>Admit a variety of deduction relations, and that the deductively closed sets</p><p>generated by some initial set of conditionals can be calculated</p><p>Extend the ordinary function operations of sum, difference, product &amp;</p><p>quotient to real-valued functions with possibly different or overlapping</p><p>domains of definition</p><p>Represent &amp; simplify complex conditional statements in Bayesian expert</p><p>systems used to calculate <em>maximum information entropy </em>solutions</p><p>Explicate the logic of quantum measurements by better expressing the</p><p>changing conditions in quantum mechanics</p>