  A new computational method is presented to implement the system of deductive
logic described by Aristotle in Prior Analytics. Each Aristotelian problem is
interpreted as a parametric probability network in which the premises give
constraints on probabilities relating the problem's categorical terms (major,
minor, and middle). Each probability expression from this network is evaluated
to yield a linear function of the parameters in the probability model. By this
approach the constraints specified as premises translate into linear equalities
and inequalities involving a few real-valued variables. The problem's figure
(schema) describes which specific probabilities are constrained, relative to
those that are queried. Using linear optimization methods, the minimum and
maximum feasible values of certain queried probabilities are computed, subject
to the constraints given as premises. These computed solutions determine
precisely which conclusions are necessary consequences of the premises. In this
way, Aristotle's logical deductions can be accomplished by means of numerical
computation.
