Theorey of vector truth degrees of formulas in two-valued predicate logic

Quantitative logic, which sets up certain ways of connection between mathematical logic and numerical computation, is regarded as a highly representative example of uncertainty that is capable of handling vagueness. In this paper, the definition of the vector truth degree of first-order formulae and the definition of the vector similarity degree between first-order formulae are proposed, along with their properties being discussed respectively. The proposed work enriches the theory of quantitative predicate logic, and provides a possible framework of approximate reasoning that is able to catch both the qualitative and quantitative aspects of the real problem.