TikZ diagram, placement of nodes, dotted line

Question

This is my very first TikZ diagram, so please bear with my beginner's ignorance of things that are probably very basic. I'm trying to get a diagram close to the following:

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{matrix}
\begin{document}
\begin{tikzpicture}
\matrix[matrix of nodes,
    column 1/.style={anchor=east,align=right,color=purple},
    column 2/.style={anchor=center,text centered,align=center},
    column 3/.style={anchor=center,text centered,align=center},
minimum width=2cm,minimum height=2cm] (a) {

row1 & \node[draw]{text1}; & \node[draw]{text2}; \\
row2 & \node[draw]{double\\text3}; & \node[draw]{text4}; \\
{} & \node[anchor=south]{col1}; & \node[anchor=south]{col2}; \\
};
  \node at (1,2.5) [fill=white!100] {\emph{is}};
  \node at (1,0.5) [fill=white!100] {\emph{is not}};
\end{tikzpicture}
\end{document}

Which gives me:

Which is almost what I want. But, I was trying to get the column desriptions closer to border of the node above, and couldn't figure it out. I know from the pgf-manual that in order to move it up I have to use the "south" anchor but for some reason it wouldn't move.

The second thing (clarified):
The vertical border between node "text1" and node "text2" should not be drawn and in the row below the vertical border between node "text3" and node "text4" should be a dotted line.

Any help much appreciated!

Answer 1

After your clarification I would suggest this:

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{matrix}
\usetikzlibrary{positioning,calc}
\begin{document}
\begin{tikzpicture}[% define styles for row labels and col labels here
    row style/.style={color=purple},%
    col style/.style={},%
]
\matrix[matrix of nodes,%
    column 1/.style={anchor=center,text centered,align=center},%
    column 2/.style={anchor=center,text centered,align=center},%
    minimum width=2cm,minimum height=2cm] (m) {%
  text1 &  text2 \\
  text3 &  text4 \\
};
  % column labels
  \node[col style,below=2mm of m-2-1] {col1}; 
  \node[col style,below=2mm of m-2-2] {col2};

  % row labels
  \node[row style,left=2mm of m-1-1] {row1}; 
  \node[row style,left=2mm of m-2-1] {row2};  

  % border around matrix
  \draw (m-1-1.north west) rectangle (m-2-2.south east); 

  % vertical dotted line
  \draw[dotted] (m-2-1.north east) -- (m-2-1.south east);

  % horizontal line
  \draw (m-1-1.south west) -- (m-1-2.south east);

  % place label between text1 and text2
  \node at ($(m-1-1)!.5!(m-1-2)$) [fill=white!100] {\emph{is}};

  % place label between text3 and text4
  \node at ($(m-2-1)!.5!(m-2-2)$) [fill=white!100] {\emph{is not}};  
\end{tikzpicture}
\end{document}

Answer 2

An easy way of bringing those two nodes up is to reduce the row spacing using e.g. \\[-10pt]. See code below, with some comments here and there.

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{matrix}
\begin{document}
\begin{tikzpicture}
\matrix[matrix of nodes,
    column 1/.style={anchor=east,align=right,color=purple,minimum width=1cm}, % added minimum width=1cm here
    column 2/.style={anchor=center,text centered,align=center},
    column 3/.style={anchor=center,text centered,align=center},
    minimum width=2.5cm, % increased this to 2.5cm
    minimum height=2cm] (a) {
row1 & text1 & text2 \\  % node [-8pt] added
row2 & |[text width=15mm]| {double\\text3} & text4 \\[-15pt] % note [-15pt] added
{} & col1 & col2 \\
};



\draw (a-2-2.south west) rectangle (a-1-3.north east); % draw border around cells
\draw (a-1-2.south west) -- (a-1-3.south east); %  line between rows
\draw [dashed] (a-2-2.north east) -- (a-2-2.south east); % dashed vertical line

% place is,is not nodes midway between the text nodes
\node [fill=white!100] at (a-1-2.east) {\emph{is}};
\node [fill=white!100,align=center,font=\em] at (a-2-2.east) {is\\not};
\end{tikzpicture}
\end{document}