Is there a logic symbol for counterfactuals

Question

I am looking for a symbol that looks like: []-->

So far I came up with $\Box\rightarrow$. The problem with this is, that the arrow is too far away from the box:

How could I achieve this so that the box is not so far away from the arrow?

Update: Solution below.

Additionally I also needed a might counterfactual:

\newcommand{\counterfactualmight}{\ensuremath{%
\mathord{\Diamond}\kern-1.5pt
\raise0.5pt\hbox{$\mathord{\rightarrow}$}}}

Update 2: Better Solution From http://www.ctan.org/pkg/comprehensive

%..
\usepackage{txfonts}
\usepackage{pxfonts}
%..
\begin{enumerate}
 \item A conditional: X $\rightarrow$ Y
 \item A strict conditional: X $\strictif$ Y
 \item A would-counterfactual conditional: X $\boxright$ Y
 \item A might-counterfactual conditional: X $\Diamondright$ Y
\end{enumerate}

Answer 1

A combination of \kern, \raise, \hbox, and \mathord (the final one to change the status of \rightarrow to "ordinary") should do the trick of aligning \Box and \rightarrow:

\documentclass{article}
\usepackage{amssymb}
\newcommand{\counterfactual}{\ensuremath{%
  \Box\kern-1.5pt
  \raise1pt\hbox{$\mathord{\rightarrow}$}}}
\begin{document}
$\Box\rightarrow$ vs.\ \counterfactual
\end{document}

---

Addendum: I don't know if you intend to use the \counterfactual macro in text or math mode. (That was also, by the way, why I used \ensuremath to encase the macro's contents.) If you intend to use it in math mode, it may be a good idea to give it "mathrel" (relational operator) status, e.g., by defining it as

\newcommand{\counterfactual}{\ensuremath{%
  \mathrel{\Box\kern-1.5pt\raise1pt\hbox{$\mathord{\rightarrow}$}}}}

That way, the spacing in expressions such as $A \counterfactual B$ will be correct without need for further fiddling.

Answer 2

There's no need to guess or measure things, other than the amount of back up. The arrow should be at the same height as plain arrows. So we can use the fact that \mathop applied to a single object centers it with respect to the math axis.

\documentclass{article}
\usepackage{amssymb}
\newcommand{\counterfactual}{%
  \mathrel{\mathop\Box}\mathrel{\mkern-2.5mu}\rightarrow
}
\newcommand{\mightcounterfactual}{%
  \mathrel{\mathop\Diamond}\mathrel{\mkern-2.8mu}\rightarrow
}

\begin{document}
$A\counterfactual B$

$A\mightcounterfactual B$

$\counterfactual_{\counterfactual}
 \mightcounterfactual_{\mightcounterfactual}$
\end{document}