This paper aims to establish the semantic of 2n valued propositional calculus (2nP) in order to set the logical foundation of big data science. This paper specifies the truth value form of 2n valued logic and uses bit structure to characterize the functions of connectives, and set valuation mapping of 2nP. In light of the features of 2nP and by taking key-value data model and data redundancy as examples, this paper intuitively discusses the effects of 2nP applied to the researches on big data. Furthermore, this paper initially analyzes the relationship between semantic of classic propositional logic and the one of 2nP, and shows the 2nPs application perspectives on computer science, information techniques, and artificial intelligence.