In the paper, the general theory of semantical triangle is developed. Fundamental notions of correspondence in Frege’s triangle, metalogical possibility, logical possibility, and fact are introduced. There are only 7 metalogical possibilities, so they all are described. On the basis of treatment the sense as a function the theory of abstract semantical valuations is developed. This theory implies two well-known theories, i. e. existence theory and truth function theory, because we can treat existence of individuals and truth functions as abstract semantical valuations defined on the basis of Frege’s triangle. So, the theory of Frege’s triangle can explain what is existence and can be a fundament for the correspondence theory of truth. At last, the notions of logical possibility and factual possibility are distinguished.