恩德顿的等价符号

Question 1

这是一张图片（由谷歌图书）

代码可能是

\documentclass{article}
\usepackage{amsmath,amssymb}
\usepackage{graphicx}

\newcommand{\tautimplies}{\vDash}
\newcommand{\tautimplied}{\mathrel{\text{\reflectbox{$\vDash$}}}}
\newcommand{\tauteq}{%
  \tautimplies
  \mathrel{\mspace{1mu}}%
  \tautimplied
}

\begin{document}

If \(\Sigma\) is singleton \(\{\sigma\}\), then we write
``\(\sigma \tautimplies \tau\)'' in place of 
``\(\{\sigma\} \tautimplies \tau\).'' If both \(\sigma \tautimplies \tau\) and
\(\tau \tautimplies \sigma\), then \(\sigma\)  and \(\tau\) are said to be 
\emph{tautologically equivalent} (written \(\sigma \tauteq \tau\)).
For example, in Section 1.0 we encountered the wffs
\( (\lnot(\mathbf{C} \lor \mathbf{K})) \) and
\( ((\lnot\mathbf{C}) \land (\lnot\mathbf{K})) \)
as alternative translations of an English sentence.  We can now assert that
they are tautologically equivalent.

\end{document}

Answer

这是一张图片（由谷歌图书）

代码可能是

\documentclass{article}
\usepackage{amsmath,amssymb}
\usepackage{graphicx}

\newcommand{\tautimplies}{\vDash}
\newcommand{\tautimplied}{\mathrel{\text{\reflectbox{$\vDash$}}}}
\newcommand{\tauteq}{%
  \tautimplies
  \mathrel{\mspace{1mu}}%
  \tautimplied
}

\begin{document}

If \(\Sigma\) is singleton \(\{\sigma\}\), then we write
``\(\sigma \tautimplies \tau\)'' in place of 
``\(\{\sigma\} \tautimplies \tau\).'' If both \(\sigma \tautimplies \tau\) and
\(\tau \tautimplies \sigma\), then \(\sigma\)  and \(\tau\) are said to be 
\emph{tautologically equivalent} (written \(\sigma \tauteq \tau\)).
For example, in Section 1.0 we encountered the wffs
\( (\lnot(\mathbf{C} \lor \mathbf{K})) \) and
\( ((\lnot\mathbf{C}) \land (\lnot\mathbf{K})) \)
as alternative translations of an English sentence.  We can now assert that
they are tautologically equivalent.

\end{document}

Question 2

我猜你指的是赫伯特·恩德顿教科书第二版第 24 页上的符号，逻辑的数学导论。类似于这个符号的是 ⧦ (U+29E6)，\gleichstark在中unicode-math，以下 MWE 重现了定义它的段落：

\documentclass[varwidth=10cm, preview]{standalone}
\usepackage{mathtools}
\usepackage{unicode-math}
\usepackage{microtype}

\defaultfontfeatures{ Scale = MatchUppercase }
\setmainfont[Scale = 1.0]{STIX Two Text}
\setmathfont{STIX Two Math}

\begin{document}
If \(\Sigma\) is \(\operatorname{singleton}\{σ\}\), then we write
“\(σ \vDash τ\)” in place of “\(\{σ\} \vDash τ\).” If both \(σ \vDash τ\) and
\(τ \vDash σ\), then \(σ\)  and \(τ\) are said to be \emph{tautologically
equivalent} (written \(σ \gleichstark τ\)).
For example, in Section 1.0 we encountered the wffs
\( \left(¬\left(\symbfup C ⋁ \symbfup K\right)\right) \) and
\( \left(\left(¬\symbfup C\right) ⋀ \left(¬\symbfup K\right)\right) \)
as alternative translations of an English sentence.  We can now assert that
they are tautologically equivalent.
\end{document}

这个版本比文本中的版本要窄一些，但你可以用另一种字体寻找更宽的版本。你也可以使用这个定义：

\newcommand\tautequiv{\mathrel{\vDash \mkern -2.5mu \Dashv}}

使用 STIX Two Math 作为数学字体，可得出以下结果：

有些数学字体缺少可用的\Dashv，在这种情况下您可以粘贴来\reflectbox{$\vDash$}代替：

\documentclass[varwidth=10cm, preview]{standalone}
\usepackage{mathtools}
\usepackage{unicode-math}
\usepackage{microtype}
\usepackage{graphicx}

\defaultfontfeatures{ Scale = MatchUppercase }
\setmainfont[Scale = 1.0]{TeX Gyre Pagella}
\setmathfont{Asana Math}

\newcommand\tautimpl{\vDash}
\newcommand\tautequiv{\mathrel{\vDash \mkern -2.25mu
                               \mathrel{\reflectbox{\ensuremath\vDash}}}}
%\newcommand\tautequiv{\gleichstark}

\begin{document}
If \(\Sigma\) is \(\operatorname{singleton}\{σ\}\), then we write
“\(σ \tautimpl τ\)” in place of “\(\{σ\} \tautimpl τ\).” If both
\(σ \tautimpl τ\) and \(τ \tautimpl σ\), then \(σ\)  and \(τ\) are said to be
\emph{tautologically equivalent} (written \(σ \tautequiv τ\)).
For example, in Section 1.0 we encountered the wffs
\( \left(¬\left(\symbfup C ⋁ \symbfup K\right)\right) \) and
\( \left(\left(¬\symbfup C\right) ⋀ \left(¬\symbfup K\right)\right) \)
as alternative translations of an English sentence.  We can now assert that
they are tautologically equivalent.
\end{document}

就我有限的德语水平而言，格莱希·斯塔克字面意思是“同样强烈”，但暗示“非常平衡”。

如果您需要使用 PDFTeX 而不是 LuaLaTeX 或 XeLaTeX，请尝试加载包stix2，用替换\symbfup，\mathbf并可能拼出剩余的非 ASCII 符号。

Answer