The Discovery of Logical Propositions in Numerical Data

Abstract

Statisticians deal with numerical data, but they do not discover logical propositions in the numerical data. This paper presents a method to discover logical propositions in numerical data. The author presented a topological model for non-classical logics. The author also showed that the extended model is a Euclidean space and the orthonormal system is the logical functions corresponding to the atoms in Boolean algebra. The method presented in this paper is based on this topological model for logics. A function obtained by multiple regression analysis in which data are normalized to [O, 1] belongs to this Euclidean space. Therefore, the function represents a non-classical logical proposition and it can be approximated by a classical logical function representing a classical logical proposition. The algorithm is as follows. 1. The numerical data are normalized to [0, 1]. 2. Multiple regression analysis is performed. 3. The result is a logical function of nonclassical logics, and it is approximated by a classical logical function. 4. The classical logical proposition is reduced to the minimum one. We show that the classical propositions obtained by this method can not be always obtained by the other methods. Experimental results show that this algorithm works well in general. However, another algorithm is presented, because this algorithm does not work well sometimes. This method will be applied to the discovery of logical propositions in numerical data.