Abstract
The aim of this paper is the partial axiomatization for universal logic which was proposed by Prof H.C. He in 2001. Firstly, a propositional calculus formal deductive system UL <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">hisin(0,1)</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Delta</sup> for 0-level universal AND operator is built up. Secondly, the corresponding algebra LstrokPiG <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Delta</sub> is introduced. Finally, we prove the system UL <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">h</sub> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">isin(0,1) </sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Delta</sup> is sound and complete
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