A Nonclassical Logical Model for the Representation of Uncertain Knowledge

Abstract

This paper presents a nonclassical logical model for the representation of uncertain knowledge. This paper is theoretically based on logic-probability dualism instead of logic monism. Firstly, the author shows that there is a correspondence between classical logic and the probability of independent events. This correspondence is extended to non-independent events. Consequently, a model for nonclassical logics is obtained. This model can be made into a Euclidean space, therefore logical functions can be represented as vectors (logical vectors). An information is introduced on the Iogical vectors. The author proves the information equals the ordinary information. A transformation formula from probability vectors to logical vectors is introduced. Due to these concepts, the discussion on the representation of uncertain propositions are possible.