The Discovery of Logical Propositions in Numerical Data

Hiroshi Tsukimoto

This paper presents a method to discover logical propositions in numerical data. The method is based on the space of multi-linear functions, which is made into a Euclidean space. A function obtained by multiple regression analysis in which data are normalized to [0,1] belongs to this Euclidean space. Therefore, the function represents a non-classical logical proposition and it can be approximated by a Boolean function representing a classical logical proposition. We prove that this approximation method is a pseudo maximum likelihood method using the principle of indifference. We also experimentally confirm that correct logical propositions can be obtained by this method. This method will be applied to the d.iscovery of logical propositions in numerical data.

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