確率分布の直観主義論理による推論

抄録

Several studies have been carried out with the objective of introducing partial orders into probability distributions. However, there has been no study that introduces such a partial order into probability distributions as can be reasoned by a logic. This paper shows that discrete probability distributions can be reasoned by intuitionistic logic. The space of multi-linear functions, which is an extension of Boolean algebra, can be made into a Euclidean space. The space is Heyting algebra, which is the model of intuitionistic logic. Therefore, multi-linear functions can be reasoned by intuitionistic logic. Discrete probability distributions can be corresponded to multi-linear functions using the principle of indifference. So discrete probability distributions can be reasoned by intuitionistic logic.