# Symbol for skeptical consequence

I'm looking for a symbol for skeptical consequence so that I can write that something, B, is a skeptical consequence of something else, A.

In a book I read it's written like $$A \vdash B$$ or $$A \sststile{}{} B$$ but the horizontal line is wavy like \sim, has the same width as the vertical line and does not vary in width. So, what I'm looking for is a binary relation symbol that is similar to the combination of the first two and the last relation in the following image:

That is, something similar to the following mockup but the wavy line should be such that it has a constant width and the same width as the vertical line:

I've tried Detexify without success.

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Well, there's always the Big List you can try: ctan.org/tex-archive/info/symbols/comprehensive –  Ulrich Schwarz Oct 13 '11 at 14:12
ugly way: $|\!\!\!\sim$. This might not scale well... –  Roelof Spijker Oct 13 '11 at 14:20
@N.N.: Unable to find it anywhere in the comprehensive list... –  DevSolar Oct 13 '11 at 14:31
Best I've found as yet is ⍭ –  Loop Space Oct 13 '11 at 14:42
There's a follow up to this question at tex.stackexchange.com/questions/32244/… –  N.N. Oct 25 '11 at 7:18

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.

\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:

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

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The book I found the symbol in treats the same topic as the article you link, that is, default logic. I think what would look best is having them connected but the wavy sign being constant in width and having the same width as the vertical line. –  N.N. Oct 13 '11 at 15:15
@N.N.: Have updated the solution where the vertical and wavy lines touch and both get resized. –  Peter Grill Oct 13 '11 at 23:08
Maybe it would be more correct to define the symbol with \mathrel rather than \mathbin? It expresses a relation rather than an operation. But maybe I'm wrong, my only knowledge of types of math symbols is from tex.stackexchange.com/questions/21336/… –  N.N. Oct 19 '11 at 21:20
Good point. Have updated it to use \mathrel. Also took this opportunity to fix the horizontal spacing issue present in the earlier solution. –  Peter Grill Oct 19 '11 at 21:40
In the equation with \dfrac the left edge of \sim is noticeable but it's not in the other equations. Is this possible to fix? –  N.N. Oct 20 '11 at 6:19

The following uses \medvert and a clipped version of \sim from the MnSymbol package. Clipping is provided by adjustbox's \clipbox:

\documentclass{article}
\usepackage{MnSymbol}% http://ctan.org/pkg/mnsymbol
\usepackage{amsmath}% http://ctan.org/pkg/amsmath
\begin{document}
\newcommand*{\skepcon}{\ensuremath{\mathrel{\medvert\mskip-5.7mu\clipbox{1 0 0 0}{$\sim$}}}}
$A\skepcon B$
\end{document}


These two symbols have the same fixed width, as opposed to the varied width of \sim when not loading MnSymbol.

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Is it possible to fix so that the left bottom edge of \sim is not not noticable as it merges with \medvert? I want them to look as they're one symbol rather than two merged. –  N.N. Oct 20 '11 at 7:37
@N.N.: I've updated my answer to clip the \sim symbol using adjustbox's \clipbox macro. –  Werner Oct 20 '11 at 7:46

This site recommends:

\newcommand{\nc}{\,\mid\!\sim\,}


Though perhaps it would be worth wrapping it in a \mathrel or something for proper spacing?

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