The axiomatization for 0-level universal logic

Authors:
Yingcang Ma;Huacan He
Affiliations:
College of Science, Xi’ an University of Engineering Science and Technology, Xi’an, China;School of Computer Science, Northwestern Polytechnical University, Xi’ an, China
Venue:
ICMLC'05 Proceedings of the 4th international conference on Advances in Machine Learning and Cybernetics
Year:
2005

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Abstract

The aim of this paper is the partial axiomatization for 0-level universal logic. Firstly, a propositional calculus formal deductive system UL$_{h{\it \epsilon}[0,1]}$ of 0-level universal logic is built up, and the corresponding algebra Ł ΠG is introduced. Then we prove the system UL$_{h{\it \epsilon}[0,1]}$ is sound and complete with respect to the 0-level continuous universal AND operators on [0, 1]. Lastly, three extension logics of UL$_{h{\it \epsilon}[0,1]}$ are also introduced.