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《Journal of Nanjing University of Aeronautics & Astronautics》 1993-05
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Algorithm and Its Applications of Transformation between Medium Predicate Calculus Systems ME and ME

Zhang Dongmo (Department of Computer Science and Engineering, NUAA Nanjing, 210016)Xiao Xian (Department of Mathematics of Nanjing Airforce Meteorological Academy Nanjing,210012)Zhu Wujia (Department of Computer Science and Engineering,NUAA Nanjing,210016)  
In classical 2-valued logic,it is known that the connective system of predicate calculus with equality ,FI are equivalent to that of FI , these two systems are also equivalent under the relationship of inference. In medium logic (ML), however, it has been proved that the connective systems of medium predicate calculus ME and ME are not e-quivalent. Theorem 1 in this paper gives an algorithm which transforms a formula of ME into a prenex standard form in ME,and therefore shows that ME is equivalent to ME under the relationship of inference. As a special sub-system of ML, ME has many useful properties similar to those in 2-valued logic. The result shown above provides a foundation for the generalization of these properties onto ME. As two examples, we present the Skolem standard form theorem and the Herbrand theorem of ME. The results in the paper also show that the equivalence between two logic systems under the relationship of inference does not means that they have the same logical properties.
【Fund】: 国家自然科学基金
【CateGory Index】: O141
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【Co-citations】
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【Co-references】
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