Research On The Theory Of Incomplete Information Database

Incomplete information database is an important field in database theory. It does not only have important theoretical values, but also has great practical values. Nowdays, there are not an improved theory system for representing and dealing with incomplete information. The medium logic propositional calculus system MPM and the medium logic predicate calculus system MFM is a new logic system modified from the existing medium logic system. This system is fit for dealing with incomplete information. It can act as the theory foundation for dealing with incomplete information. In this paper, a new type algebra is introduced, it is the algebraic abstract of MPM system just as Boolean algebra is the algebraic abstract of 2-valued propositional calculus. The main purpose of this paper is to investigate the various properties of the new algebra. In addition, this paper constructs an axiom set based on the medium logic propositional calculus system MPM, and gives a proof of its completeness. This axiom set consists of fifteen equations, and it is easier to prove and deduce the identity equations of the MPM system. Then, this paper introduces the concept of truth degrees of propositions based on the probability space in MPM logic system and discusses some properties. It is proved that general reference rules with truth degrees are hold in MPM logic system. At last, this paper discusses 3-valued logic, points out some deficiencies of 3-valued logic system, and establishes a propositional logic system with 4 values: true, false, divergent and meaningless. Then this paper proves that this 4-valued logic system is truth-functionally complete, and expands its connective.