Propositional Sequent Calculus With List Construction And Addition

摘要

To formalize the tasks for the implementation of information systems, a propositional sequent calculus for extended formulas is proposed. The definition of an extended formula has two additional assertions:rn(1) The extended formula which is an equality of two linear combinations of the extended formulas and of all list elements.where each element is a linear combination of an extended formulas,rn(2) The extended formula is "the value of linear combination of the extended formulas belongs to the list of values of the linear combination of extended formulas".rnRational numbers are used for linear combination coefficients. This is more convenient to computer models. The extended formulas are suitable to describe the idea of perception. The proposed sequent calculus may be used to represent an essential knowledge for information systems. For example, junction can be easily described by using the extended formula. It has been proved that the proposed calculus is sound and complete.