With an illustrative example of $$5 \times 3 = 5 \times 3 $$, the first section explained the major problem in the natural language interpretation process. The second section introduced Frege’s famous idea of ‘sense’. And this paper argues that Frege’s definition is not constructive. The Third section contributes a subtle amendment to the syntax of IL (Intentional Logic). Traditionally, the three basic types e, t and s were not treated as a part of vocabulary of IL, while this paper argues that this treatment has allowed a much explicit way to coding programs in real algorithm. Given this treatment, “an expression $$\alpha $$ of type $$\tau $$” is shortened to “$$\alpha |\tau $$”. In the end of section three, this paper gave a natural language sentence to illustrate the intention and extension operators. And furthermore, there comes the analyses of information preservation ability of these operators.