[Tex/LaTex] Symbol for skeptical consequence that matches the turnstile package

math-operatorsrelation-symbolssymbolsturnstile

This might be seen as a follow up to Symbol for skeptical consequence. From it I got answers so that I could write that B is a skeptical consequence of A such as

B is a skeptical consequence of A

which Peter Grill's code produces. Now say that I use the turnstile package to typeset turnstiles which symbolizes logical consequence, that I prefer the turnstiles of the turnstile package to \vdash and \vDash, and that I in the same text want to speak both of logical and skeptical consequence. Then I face two problems:

The turnstiles of the turnstiles package don't match any of the symbols for skeptical consequence in the answers of Symbol for skeptical consequence because the turnstiles of the turnstile package are larger.
The turnstiles of the turnstile package is superior in how symbols are placed below the turnstile.

This can be illustrated by the following which symbolizes that B is a skeptical consequence of A in language L and that B is a logical consequence of A in language L:

B is a logical and skeptical consequence of A

What I would like is, ideally, an extension of the turnstile package to handle skeptical consequence so that I could produce turnstiles with a wavy horizontal that matches the (normal) turnstiles, both in terms of appearance and ability to have correctly placed symbols below and above, of the turnstile package. Also, in contrast to what the images shows, I'd like the wavy line to be such that it has the same thickness and edges as the vertical line.

Best Answer

The turnstile package provides

\turnstile[<size>]{<lvert>}{<horz>}{<below>}{<above>}{<rvert>}

where <horz> calls the macro

\makehor{<line type>}{<thickness>}{<length>}{<sep>}

to draw the horizontal line(s) of the turnstile. In the following code, I've redefined \makehor (and consequently also \turnstile) to take a first argument w (for wavy) which typesets the symbol $\sim$ as the "horizontal line". The adjustbox package provides some clipping and resizing.

enter image description here

\documentclass{article}
\usepackage{turnstile}% http://ctan.org/pkg/turnstile
\usepackage{adjustbox}% http://ctan.org/pkg/adjustbox

\renewcommand{\makehor}[4]
  {\ifthenelse{\equal{#1}{n}}{\hspace{#3}}{}
   \ifthenelse{\equal{#1}{s}}{\rule[-0.5#2]{#3}{#2}}{}
   \ifthenelse{\equal{#1}{d}}{\setlength{\lengthvar}{#2}
     \addtolength{\lengthvar}{0.5#4}
     \rule[-\lengthvar]{#3}{#2}
     \hspace{-#3}
     \rule[0.5#4]{#3}{#2}}{}
   \ifthenelse{\equal{#1}{t}}{\setlength{\lengthvar}{1.5#2}
     \addtolength{\lengthvar}{#4}
     \rule[-\lengthvar]{#3}{#2}
     \hspace{-#3}
     \rule[-0.5#2]{#3}{#2}
     \hspace{-#3}
     \setlength{\lengthvar}{0.5#2}
     \addtolength{\lengthvar}{#4}
     \rule[\lengthvar]{#3}{#2}}{}
   \ifthenelse{\equal{#1}{w}}{% New wavy $\sim$ definition
     \setbox0=\hbox{$\sim$}%
     \raisebox{-.6ex}{\hspace*{-.05ex}\adjustbox{width=#3,height=\height}{\clipbox{0.75 0 0 0}{\usebox0}}}}{}
  }

\begin{document}

\[
  \renewcommand{\arraystretch}{2}%
  \begin{array}{ll}
    \textrm{Regular}\ \verb!s! & \textrm{Wavy}\ \verb!w! \\ \hline
    A\turnstile{s}{s}{}{}{n}B & A\turnstile{s}{w}{}{}{n}B \\
    A\turnstile{s}{s}{L}{}{n}B & A\turnstile{s}{w}{L}{}{n}B \\
    A\turnstile{s}{s}{}{D}{n}B & A\turnstile{s}{w}{}{D}{n}B \\
    A\turnstile{s}{s}{L}{D}{n}B & A\turnstile{s}{w}{L}{D}{n}B
  \end{array}
\]
\end{document}

The main advantage of tapping into the existing command (or extending it) rather than writing one's own is that it is easier to use. Additionally, since \turnstile takes the upper/lower letters as arguments, it's easier to grab hold of them than (say) defining a new command that requires some interpretation of limit use, like \wavyturn_{L}^{D} (say). As such, the other features of \turnstile is adopted (like the \rule for the vertical line and the other spacing.

The above code currently only works for a single wavy line. However, if needed, it could be extended to work for more than one (like the original \turnstile..{d}... and \turnstile..{t}.. commands). For now, it works based on the MWE, but not work as expected with other variations (longer phrases and/or right vertical line). That may require more work, since I haven't tested it.

Edit: Admittedly my tikz-prowess requires a heavy boost of steroids. The following addition to the turnstile horizontal rule is provided by the symbol z. It draws a thin wavy line using a sine curve. I'm pretty sure the horizontal (\hspace) and vertical (\raisebox) adjustments can be done inside \tikz, so suggestions are welcome and encouraged. The same goes for the adjustbox modifications, and whether that can be incorporated in \tikz as well:

enter image description here

\documentclass{article}
\usepackage{turnstile}% http://ctan.org/pkg/turnstile
\usepackage{tikz}% http://ctan.org/pkg/pgf
\usepackage{adjustbox}% http://ctan.org/pkg/adjustbox

\renewcommand{\makehor}[4]
  {\ifthenelse{\equal{#1}{n}}{\hspace{#3}}{}
   \ifthenelse{\equal{#1}{s}}{\rule[-0.5#2]{#3}{#2}}{}
   \ifthenelse{\equal{#1}{d}}{\setlength{\lengthvar}{#2}
     \addtolength{\lengthvar}{0.5#4}
     \rule[-\lengthvar]{#3}{#2}
     \hspace{-#3}
     \rule[0.5#4]{#3}{#2}}{}
   \ifthenelse{\equal{#1}{t}}{\setlength{\lengthvar}{1.5#2}
     \addtolength{\lengthvar}{#4}
     \rule[-\lengthvar]{#3}{#2}
     \hspace{-#3}
     \rule[-0.5#2]{#3}{#2}
     \hspace{-#3}
     \setlength{\lengthvar}{0.5#2}
     \addtolength{\lengthvar}{#4}
     \rule[\lengthvar]{#3}{#2}}{}
   \ifthenelse{\equal{#1}{w}}{% New wavy $\sim$ definition
     \setbox0=\hbox{$\sim$}%
     \raisebox{-.6ex}{\hspace*{-.05ex}\adjustbox{width=#3,height=\height}{\clipbox{0.75 0 0 0}{\usebox0}}}}{}
   \ifthenelse{\equal{#1}{z}}{% New tikz wavy definition
     \raisebox{-.4ex}{\hspace*{-.08ex}\tikz \draw [thin,x=0.5ex,y=.25ex] (0,0) sin (1,1) cos (2,0) sin (3,-1) cos (4,0);\hspace*{.2ex}}}{}   
  }

\begin{document}

\[
  \renewcommand{\arraystretch}{2}%
  \begin{array}{lll}
    \textrm{Regular}\ \verb!s! & \textrm{Wavy}\ \verb!w! & \textrm{TikZ}\ \verb!z! \\ \hline
    A\turnstile{s}{s}{}{}{n}B & A\turnstile{s}{w}{}{}{n}B & A\turnstile{s}{z}{}{}{n}B \\
    A\turnstile{s}{s}{L}{}{n}B & A\turnstile{s}{w}{L}{}{n}B & A\turnstile{s}{z}{L}{}{n}B \\
    A\turnstile{s}{s}{}{D}{n}B & A\turnstile{s}{w}{}{D}{n}B & A\turnstile{s}{z}{}{D}{n}B \\
    A\turnstile{s}{s}{L}{D}{n}B & A\turnstile{s}{w}{L}{D}{n}B & A\turnstile{s}{z}{L}{D}{n}B
  \end{array}
\]
\end{document}

It needs improvement for a number of reasons:

There is a very minute difference in the typesetting of a "denominator-only" and "numerator+denominator" \turnstile. For example, look at the close-up between
Unexpected results may occur from adding the ending vertical line(s).
The spacing of the right operand (B in this case) is too far off. This can be accommodated by means of an intermediate macro, but it is best suited inside the \turnstile macro.

I think all of the above items would be addressed by someone with a better handle on tikz-related commands. But then again, perhaps this is not a problem.

Related Solutions

[Tex/LaTex] Turnstile package

The problem with the vertical scaling is documented in the Conclusions section of the file turnstile_article.pdf:

For a future version of this package, we want to look at changing the height of the turnstile sign. This will take into account the heights of the expressions above and below, similar to the way we currently allow for the widths of the expressions.

In particular, since no provision is made for vertical scaling, the symbol will not scale appropriately when used in a subscripted expression (See first part of the example below).

The first idea that comes to my mind is to use \scalebox (from the graphicx) package to scale the turnstile symbol. The following example shows both the actual behaviour with no vertical scaling, and the definition and use of a new command attempting to alleviate this problem; of course, feel free to make the modifications that best suit your needs:

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

\newcommand*\Subsststile[2]{%
  \,\scalebox{0.8}[0.5]{$\sststile[ss]{\textstyle#1}{\textstyle#2}$}\,
}

\begin{document}

The standard command with no vertical scaling:
\[
  A_{\Gamma\sststile[ss]{}{}P} \qquad A_{\Gamma\sststile[ss]{aaaa}{b}P} 
\]

The newly defined command, with vertical scaling:
\[
  A_{\Gamma\Subsststile{}{}P} \qquad A_{\Gamma\Subsststile{aaaa}{b}P} 
\]

\end{document}

turnstile example

[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

Best Answer

Related Solutions

[Tex/LaTex] Turnstile package

[Tex/LaTex] Symbol for skeptical consequence

Related Question