用参数概率和线性最优化计算亚里士多德逻辑
Aristotle's Logic Computed by Parametric Probability and Linear Optimization
摘要：
本文提出了一种新的计算方法来实现亚里士多德在先验分析中所描述的演绎逻辑系统。每一个亚里士多德问题被解释为一个参数概率网络，其中的前提给出了与问题的分类项（主要，次要和中间）相关的概率约束。对来自该网络的每个概率表达式进行评估以产生概率模型中的参数的线性函数。通过这种方法，指定为前提的约束转化为线性等式和不等式，涉及一些实值变量。问题的图（模式）描述了相对于被查询的概率，哪些特定的概率受到约束。使用线性最优化方法，在给定的约束条件下，计算某些查询概率的最小和最大可行值。这些计算出的解精确地决定了哪些结论是前提的必然结果。这样，亚里士多德的逻辑推理就可以借助于数值计算来完成。
英文摘要：
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.
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