Theory of (n) truth degrees of formulas in modal logic and a consistency theorem

The theory of （n） truth degrees of formulas is proposed in modal logic for the first time. A consistency theorem is obtained which says that the （n） truth degree of a modality-free formula equals the truth degree of the formula in two-valued propositional logic. Variations of （n） truth degrees of formulas w.r.t. n in temporal logic is investigated. Moreover, the theory of （n） similarity degrees among modal formulas is proposed and the （n） modal logic metric space is derived therefrom which contains the classical logic metric space as a subspace. Finally, a kind of approximate reasoning theory is proposed in modal logic.

Theory of truth degrees of formulas in Lukasiewicz n-valued propositional logic and a limit theorem

The concept of truth degrees of formulas in Lukasiewicz n-valued propositional logic Ln is proposed. A limit theorem is obtained, which says that the truth function τ-n induced by truth degrees converges to the integrated truth function τ when n converges to infinite. Hence this limit theorem builds a bridge between the discrete valued Lukasiewicz logic and the continuous valued Lukasiewicz logic. Moreover, the results obtained in the present paper is a natural generalization of the corresponding results obtained in two-valued propositional logic.

Theory of truth degrees of propositions in the logic system Ln^＊

By means of infinite product of uniformly distributed probability spaces of cardinal n the concept of truth degrees of propositions in the n-valued generalized Lu- kasiewicz propositional logic system Ln^＊ is introduced in the present paper. It is proved that the set consisting of truth degrees of all formulas is dense in [0,1], and a general expres- sion of truth degrees of formulas as well as a deduction rule of truth degrees is then obtained. Moreover, similarity degrees among formulas are proposed and a pseudo-metric is defined therefrom on the set of formulas, and hence a possible framework suitable for developing approximate reasoning theory in n-valued generalized Lukasiewicz propositional logic is established.

Infimum Properties Differ in the Weak Truth-table Degrees and the Turing Degrees

We prove that there are non-recursive r.e.sets A and C with A<T C such that for every set F(?)T A,C∩F≡w(?).

Randomization of classical inference patterns and its application

By means of randomization, the concept of D-randomized truth degree of formulas in two-valued propositional logic is introduced, and it is proved that the set of values of D-randomized truth degree of formulas has no isolated point in [0,1]. The concepts of D-logic pseudo-metric and D-logic metric space are also introduced and it is proved that there is no isolated point in the space. The new built D-randomized concepts are extensions of the corresponding concepts in quantified logic. Moreover, it is proved that the basic logic connectives are continuous operators in D-logic metric space. Lastly, three different types of approximate reasoning patterns are proposed.

Application type identification of Internet flows based on medium mathematics

Internet application identification is needed by network management in many aspects,such as quality of service （QoS） management,intrusion detection,traffic engineering,accounting,and so on. This article makes an in-depth study of precise identification of Internet applications by using flow characteristics instead of well-known port or application signature match. A novel approach that identifies the application type of an Internet protocol （IP） flow by finding what flow the flow looks the most like based on medium mathematics system （MMS） is proposed. The approach differs from previous ones mainly in two aspects：it has inherent scalability due to its use of the measure of n-dimensional medium truth degree; not only features of a flow,but also the association between the flow and the other flows of the same host as well as the relation among all flows of a host are employed to recognize a flow＇s application type. For the present,some popular applications are concentrated on,and up to six application types can be identified with better accuracy. The results of experiments conducted on Internet show that the proposed methodology is effective and deserves attention.