[Tex/LaTex] What command to use for reversed $\vDash$

logicsymbols

I want to use a symbol similar to

$\vDash$

but reversed (like if it's mirrored against an imaginary vertical line). I cannot find such a symbol anywhere. I have used detexify too but no luck there either.

Do you know what command and package I should use?

Best Answer

Constructed symbol

If the font does not provide the symbol, the mirroring can be done with package graphicx:

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

\makeatletter
\providecommand*{\Dashv}{%
  \mathrel{%
    \mathpalette\@Dashv\vDash
  }%
}
\newcommand*{\@Dashv}[2]{%
  \reflectbox{$\m@th#1#2$}%
}
\makeatother

\begin{document}
\[ A \vDash B \Dashv C \]
\end{document}

Remark:

The stuff with \mathpalette ensures that the symbol is properly scaled if it is used in different contexts (as index, in fractions, …).

Font package `MnSymbol`

If package MnSymbol is loaded (it also changes other math symbols), then the symbol is available as \leftmodels:

\documentclass{article}
\usepackage{MnSymbol}
\begin{document}
\[ A \leftmodels B \]
\end{document}

Font package `mathabx`

If package mathabx is used (also changes other math symbols), then the symbol is called \Dashv:

\documentclass{article}
\usepackage{mathabx}
\begin{document}
\[ A \Dashv B \]
\end{document}

Related Solutions

[Tex/LaTex] Symbol for skeptical consequence

What you describe seems similar to the nonmonotonic inference relation symbol used in this paper. The main difference being that this a small space between the two characters, which I think actually looks better than having them touch.

enter image description here

\documentclass{article}
\newcommand*{\nc}[2]{#1\mathbin{\left| \sim \vphantom{#1#2} \right.}#2}%

\begin{document}
$\nc{A}{B} \qquad \nc{\frac{A}{C}}{B}$
\end{document}

Update: Here is a version where both the straight and wavy line are re-sized and the two symbols touch:

enter image description here

I have used \scalebox from the \graphicx package to resize the symbols (resize horizontally for the wavy line and vertically for the vertical bar) based on the height of the operands on either side. The \mathrlap is obtained from a TUGboat 22 article entitled a complement to \smash, \llap, and \rlap. I am not an expert in the use of the rlap type command, so perhaps some of the resize code could be simplified. I also used pgf to do the math, and this is probably overkill but I am more familiar with that then doing math in plain TeX.

\documentclass[border=2pt]{standalone}
\usepackage{amsmath}%  only needed for \dfrac
\usepackage{graphicx}% needed for \scalebox
\usepackage{pgf}%      needed for the math calculations

% http://math.arizona.edu/~aprl/publications/mathclap/
\def\mathrlap{\mathpalette\mathrlapinternal}%
\def\mathrlapinternal#1#2{\rlap{$\mathsurround=0pt#1{#2}$}}%

\makeatletter
\newdimen\@mydimen%
\newdimen\@myHeightOfBar%
\settoheight{\@myHeightOfBar}{$|$}%
\newcommand{\SetScaleFactor}[1]{%
    \settoheight{\@mydimen}{#1}%
    \pgfmathsetmacro{\scaleFactor}{\@mydimen/\@myHeightOfBar}%
}%

\newcommand*{\Scale}[2][3]{\scalebox{#1}{\ensuremath{#2}}}%

\newcommand*{\nct}[2]{%
    \SetScaleFactor{\vphantom{\ensuremath{#1#2}}}% Compute scale to be applied
    #1%
\mathrel{\Scale[\scaleFactor]{|\mathrlap{\kern-0.48ex\sim}\hphantom{\kern-0.41ex\sim}}}%
    #2%
}%

\begin{document}
$\nct{a}{b}  \qquad \nct{\frac{A}{C}}{B}  \qquad \nct{\dfrac{A}{C}}{B}$
\end{document}

An enhanced version of this solution that allows you to specify a character to be placed above and below the wavy line is available at the follow-up question: Symbol for skeptical consequence that matches the turnstile package

[Tex/LaTex] A \(re)newcommand that does not care if a command is already defined

There is \providecommand that defines a macro if it is not yet defined. Together with \renewcommand you have your "\extranewcommand":

\providecommand{\foo}{}
\renewcommand{\foo}[1]{bar: #1}

Or you can switch to the plain TeX primitives (other syntax!), e.g.:

\long\def\foo#1{bar: #1}

(\renewcommand and friends without star use \long\def and if the star form is given, \def without \long is used. Also the parameters are specified differently.)

`\declarecommand`

A definition of the "requested" \declarecommand that calls \providecommand and \renewcommand together:

\documentclass{article}

\makeatletter
\newcommand*{\declarecommand}{%
  \@star@or@long\declare@command
}
\newcommand*{\declare@command}[1]{%
  \provide@command{#1}{}%
  % \let#1\@empty % would be more efficient, but without error checking
  \renew@command{#1}%
}
\makeatother

\begin{document}

\declarecommand*{\foo}{\typeout{foo 1: \meaning\foo}}
\foo
\declarecommand{\foo}{\typeout{foo 2: \meaning\foo}}
\foo
\declarecommand*{\foo}[1]{\typeout{foo #1: \meaning\foo}}
\foo{3}

\end{document}

Result:

foo 1: macro:->\typeout {foo 1: \meaning \foo }
foo 2: \long macro:->\typeout {foo 2: \meaning \foo }
foo 3: macro:#1->\typeout {foo #1: \meaning \foo }

Best Answer

Constructed symbol

Font package MnSymbol

Font package mathabx