确定多值命题微积分中演绎问题的一种代数方法

Proceedings of 24th International Symposium on Multiple-Valued Logic (ISMVL'94) Pub Date : 1994-05-25 DOI:10.1109/ISMVL.1994.302191

Jin-Zhao Wu, Hongyan Tan

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引用次数: 6

摘要

证明了给定多值逻辑中给定命题公式在有理数域Q上存在一个多项式。然后，判断一个命题公式是否可以从一个命题公式的有限集合中演绎出来(演绎问题)，我们只需要判断该多项式是否在与该公式集合相关的代数变量上消失。通过对该代数变量的分解，给出了求解该问题的一种算法

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An algebraic method to decide the deduction problem in many-valued propositional calculus

We show that there is a polynomial over the rational number field Q corresponding to a given propositional formula in a given many-valued logic. Then, to decide whether a propositional formula can be deduced from a finite set of such formulas (deduction problem), we only need to decide whether the polynomial vanishes on an algebraic variety which is related to this formula set. By decomposing this algebraic variety, an algorithm to decide this problem is given.<>

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Proceedings of 24th International Symposium on Multiple-Valued Logic (ISMVL'94)

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