Lukasiewicz蕴涵算子的导出算子及其n值逻辑系统L_n

N-valued logic system L_n based on the derived operator of Lukasiewicz implication operator

讨论了剩余类蕴涵算子之一Lukasiewicz蕴涵算子的导出算子的三值系统L_3和n值逻辑系统L_n(n>3),首先给出了L_3的真值表,它是C_2真值表的扩充,它也保持MP规则和正则性,接下来讨论了L_3中的重言式(tautology)与IPC(intuitionistic propositional calculus)公理之间的关系以及L_3的准重言式与C_2的重言式之间的关系。最后考虑了L_n中的子代数及不同逻辑系统L_n中重言式的比较。

This paper discussed one of the residuated class implication operators n-valued logic system （n≥ 3）based on the derived operator of Lukasiewicz implication operator. Firstly, we gave the value table on logic system L3. It is proved that the logic system L3 is a generalization of the classical logic system C2, Secondly, we discussed the relation between the tautologies in the logic system L3 and IPC （Intuitionistic propositional calends）axioms, the quasi-tautologies in the logic system L3 and the classical logic system C2. At last, the sub-algebra in the logic system L3 is investigated and compared the relation of the tautologies in some different logic systems L3.