“cyclic negation”的概念、定义、翻译、参考文献-科学参考

cyclic negation

Logic

For a logic with $n$ many truth values ${t_{0}, . . ., t_{n - 1}}$ with linearly ordered indices, a unary function $\neg$ defined by the scheme:
$\neg t_{i} = {\begin{cases} t_{i + 1} if 0 \leq i < n - 1 \\ t_{0} if i = n - 1 \end{cases}$
$n$ can be considered the period of the negation, justifying the identity
$\underset{n times}{\underset{︸}{\neg \dots \neg}} t_{i} = t_{i}$
Cyclic negation is frequently known as Post negation, after mathematician Emil Post (1897–1954), who first introduced it.

单词	cyclic negation
释义	cyclic negation Logic For a logic with $n$ many truth values ${t_{0}, . . ., t_{n - 1}}$ with linearly ordered indices, a unary function $\neg$ defined by the scheme: $\neg t_{i} = {\begin{cases} t_{i + 1} if 0 \leq i < n - 1 \\ t_{0} if i = n - 1 \end{cases}$ $n$ can be considered the period of the negation, justifying the identity $\underset{n times}{\underset{︸}{\neg \dots \neg}} t_{i} = t_{i}$ Cyclic negation is frequently known as Post negation, after mathematician Emil Post (1897–1954), who first introduced it.
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