真函数逻辑完备中的不可判定性

[1991] Proceedings of the Twenty-First International Symposium on Multiple-Valued Logic Pub Date : 1991-05-26 DOI:10.1109/ISMVL.1991.130734

Frank J. Wroblewski

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引用次数: 0

摘要

逻辑主义的早期真理规则被整合到数学的认知起源中。首先用不真不假的互补不确定值穷尽形式真条件。确定的谢弗真理授予规则的交替真理赋值并没有穷尽授予创始真理所必需的命题状态。通过完成状态分配，量子器公理以重言式的方式约简为Sheffer规则的退化结果。该完备性是推导出将二价真值表延续到三价真值表的不确定Sheffer赋予真值规则的前提条件。不可判定性降低为三种真理度之一，其替代值包括不确定性。

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Undecidability in the completion of truth-function logic

The inchoate rules of truth of logicism are cohered into the epistemic genesis for mathematics. First the formal truth conditions are exhausted with the complementary indeterminate value, not true and not false. The alternant truth assignments of the determinate Sheffer truth-conferring rules are not exhaustive of the propositional states of affairs necessary for conferring the founding truths. By completing the states-of-affairs assignments, the quantizer axioms reduce to degenerate consequents of Sheffer's rules in the manner of tautologies. The completion is prerequisite for deducing the indeterminate Sheffer truth-conferring rule which continues the bivalent truth tables to trivalence. Undecidability reduces to one of three degrees-of-truth whose alternants include the indeterminate.<>

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[1991] Proceedings of the Twenty-First International Symposium on Multiple-Valued Logic

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