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A new computational method is presented to implement the system of deductivelogic described by Aristotle in Prior Analytics. Each Aristotelian problem isinterpreted as a parametric probability network in which the premises giveconstraints on probabilities relating the problem's categorical terms (major,minor, and middle). Each probability expression from this network is evaluatedto yield a linear function of the parameters in the probability model. By thisapproach the constraints specified as premises translate into linear equalitiesand inequalities involving a few real-valued variables. The problem's figure(schema) describes which specific probabilities are constrained, relative tothose that are queried. Using linear optimization methods, the minimum andmaximum feasible values of certain queried probabilities are computed, subjectto the constraints given as premises. These computed solutions determineprecisely which conclusions are necessary consequences of the premises. In thisway, Aristotle's logical deductions can be accomplished by means of numericalcomputation.

Aristotle's Logic Computed by Parametric Probability and Linear Optimization