# [Tex/LaTex] Negated implication arrows in tikzcd

diagramstikz-cdtikz-pgf

I have four properties A, B, C, D and I am trying
to summarize the logical implications between them into a single diagram. So far
I have the following picture but I would like to have some of the implication arrows to be negated (say, the arrows from A to C, A to D, B to A, C to D and B to D).

\documentclass{article}
\usepackage{tikz-cd}

\begin{document}
\begin{tikzcd}
A
\arrow[Rightarrow, shift left=0.6ex]{d}
\arrow[Rightarrow, shift left=0.6ex]{dr}
\arrow[Rightarrow, shift left=0.6ex]{r}
& B
\arrow[Rightarrow, shift left=0.6ex]{l}
\arrow[Rightarrow, shift left=0.6ex]{d}
\\
C
\arrow[Rightarrow, shift left=0.6ex]{u}
\arrow[Rightarrow, shift left=0.6ex]{r}
& D
\arrow[Rightarrow, shift left=0.6ex]{l}
\arrow[Rightarrow, shift left=0.6ex]{ul}
\arrow[Rightarrow, shift left=0.6ex]{u}
\end{tikzcd}
\end{document}


This is likely to be strongly related to this question, but I wonder if there is a simple solution, as it is a quite common situation.

Do you want to have something like this? The credits go to percusse in his answer here.

I optimized the usage of styles a bit and enlarged the image for non touching arrows. The diagonal arrows in the middle got shorten a bit, as this will look better here.

% arara: pdflatex

\documentclass{article}
\usepackage{tikz-cd}
\usetikzlibrary{decorations.markings}
\tikzset{negated/.style={
decoration={markings,
mark= at position 0.5 with {
\node[transform shape] (tempnode) {$\backslash$};
}
},
postaction={decorate}
}
}

\begin{document}
\begin{tikzcd}[arrows=Rightarrow, column sep=1.3cm, row sep=1.3cm, every arrow/.append style={shift left=0.8ex}]
A
\arrow[negated]{d}
\arrow[negated, shorten <= 6pt,shorten >= 6pt]{dr}
\arrow{r}
& B
\arrow[negated]{l}
\arrow[negated]{d}
\\
C
\arrow{u}
\arrow[negated]{r}
& D
\arrow{l}
\arrow[shorten <= 6pt,shorten >= 6pt]{ul}
\arrow{u}
\end{tikzcd}
\end{document}