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The implication is the emphasis and difficulty in the study of logics. From the point of view of interval structure, the operations of the universal logics including interval-intersection, interval-union, interval-complement and interval-implication are redefined based on the radical models. Regularity and monotonicity of interval-implication are proved; interval-intersection and interval-implication are proved to be an adjoint pair. In the paper, operation models of the interval-implication are firstly given in the special points of h. It is very important to the further study on flexibility of the interval-logics.

The aim of this paper is partial axiomatization of universal logic. A propositional calculus formal deductive system UL/sub h/spl epsi/(0,1)/ of 0-level universal logic is built up. The corresponding algebra L/spl Pi/G is introduced. We prove the system ULh/spl epsi//sub h/spl epsi/(0,1)/ is soundness and complete w.r.t. the 0-level continuous universal AND operators (i.e. the continuous Schweizer-Sklar t-norms) on [0,1].

We call any interval [a,b] generalized interval. In the before work, the operation models of universal logic and neurons were limited in interval [0,1]. Authors mainly studied the universal logic operation models and neurons based on generalized interval [a,b]. Using the NTS norms theories, this paper established the universal logic operation models on generalized interval [a,b]. And the paper gave a new uniform neuron model of several universal logic operators on generalized interval [a,b]. It made the reasoning of universal logic neuron more flexible. It proved that the operation models and neurons were sound. The work offered important theories and models for universal logic in correlation reasoning of neural systems. It is a new way for neuron reasoning from the points of generalized NTS norms and generalized interval.

In these years, universal logic has developed greatly. As a kind of concrete universal logic, authentic logic is used to analyze the security of cryptographic protocols. This paper firstly puts forward relational conceptions and gives the structure's expression of object-oriented universal logic. Then authors analyze the logic structure's expression of authentic logic with the example: BAN logic. Using the conceptions of general correlation and general self-correlation, authors discuss the applicability and correlation of authentic logic. This work can contribute to perfecting authentic logic in artificial intelligence reasoning, and offering a new expression way of universal logic.