In unsupervised learning, no algorithm has been presented to induce an appropriate proposition from probabilistic data. Therefore methods such as brute-force search have been used. This paper presents an efficient algorithm to induce an appropriate proposition from probabilistic data. A brief outline of this algorithm follows. The probabilistic data is transformed into a probability vector. This probability vector is transformed into a logical vector. This logical vector is approximated by a classical logical vector. This classical logical vector is transformed into a classical logical proposition. This proposition is reduced to the minimum one. In this procedure, the most important step is the transformation from a probability vector to a logical vector. This transformation is possible, because 1) a proposition is represented as a vector in Euclidean space, and 2) the probability vector can be transformed into a logical vector by a correspondence between the logical vector and the probability vector. This algorithm has been obtained by the combination of the vector representation of logical proposition (= logical vector) and the correspondence between the logical vector and the probability vector. The vector representation of logical proposition is possible due to functional analysis of logical function. Experiments show that the propositions obtained by this algorithm fundamentally satisfy MDL criterion. This algorithm is very efficient compared with brute-force searches. We are applying this algorithm to several problems to obtain appropriate propositions or rules.