How to construct a logic argument with colored hline with length under control?

Question

How to construct a logic argument like this one?

I can construct it like this:

Latex of my argument:

\documentclass[10pt]{article}

\usepackage{newtxtext}
\usepackage{newtxmath}

\begin{document}
  $\begin{array}{rl}
    & p \\
    & p \to q \\
    \cline{2-2}
    \therefore & q
  \end{array}$
\end{document}

There are three things I don't know how to do: 1) how to color the hline 2) how to control the length of the hline so it does not go beyond "p \to q"? 3) how to make the therefore symbol closer to q?

Basically, I need to construct one as close as possible to the first one.

Answer 1

You can use a simple tabular and colortbl:

\documentclass{article}
\usepackage{colortbl}
\usepackage{amsmath,amssymb}
\begin{document}
  \begin{tabular}{c@{\,}l@{}} 
                         & $p$ \\
\arrayrulecolor{blue}    & $p \to q$ \\\cline{2-2}
    $\therefore$         & $q$ \\
  \end{tabular}
\end{document}

You can change the color of the line using xcolor

\documentclass{article}
\usepackage{colortbl,xcolor}
\usepackage{amsmath,amssymb}
\begin{document}
  \begin{tabular}{c@{\,}l@{}} 
                         & $p$ \\
\arrayrulecolor{blue!60!green!70}    & $p \to q$ \\\cline{2-2}
    $\therefore$         & $q$ \\
  \end{tabular}
\end{document}

Same works with arrays also (since the MWE is given using arrays):

\documentclass[10pt]{article}
\usepackage{colortbl,xcolor}
\usepackage{newtxtext}
\usepackage{newtxmath}

\begin{document}
  $\begin{array}{c@{\,}l@{}}\arrayrulecolor{blue!60!green!70}
                & p         \\
                & p \to q   \\ \cline{2-2}
    \therefore  & q
  \end{array}$
\end{document}

Answer 2

I'd define an environment for this. Adjust the spacing (I used \enspace) and the color (here blue!50) to suit you.

\documentclass{article}
\usepackage{xcolor,colortbl,array,amssymb}

\newenvironment{deduction}
  {\begin{tabular}{@{}>{$}c<{$}@{\enspace}>{$}l<{$}@{}}\arrayrulecolor{blue!50}}
  {\end{tabular}}
\newcommand{\premise}[1]{&#1\\}
\newcommand{\conclusion}[1]{\cline{2-2}\therefore&#1}

\begin{document}
\begin{deduction}
\premise{p}
\premise{p\to q}
\conclusion{q}
\end{deduction}
\end{document}

Answer 3

Another possible solution:

\documentclass{article}
\usepackage{tikz}
\usepackage{amsmath,amssymb}

\newcommand{\tikzmark}[1]{\tikz[overlay,remember picture] \node[yshift=-0.2ex]({#1}) {};}

\newcommand{\tikzhline}[3][1]{\tikz[overlay,remember picture]\draw[thick,cyan,shorten <=-{#1}pt,shorten >=-{#1}pt](#2.south)--(#3.south);}

\begin{document}
\[
\begin{array}{r@{\extracolsep{5pt}}l}
& p\\
& \tikzmark{a}p\rightarrow q\tikzmark{b}\\
\tikzhline{a}{b}
\therefore & q
\end{array}
\hspace*{0.5cm}
\begin{array}{r@{\extracolsep{7pt}}l}
& p\\
& \tikzmark{c}p\rightarrow q\tikzmark{d}\\
\tikzhline[6]{c}{d}
\therefore & q
\end{array}
\]
\end{document}

The result:

You will control the length by means of the optional parameter of \tikzhline.

Answer 4

If it is just the line that you need (assuming PDFLaTeX) the following is minimal on the requirements.

\documentclass[10pt]{article}
\usepackage{amsmath,newtxmath}
\begin{document}
\begin{align*}
                &p                                                      \\
                &p\pdfliteral{-10 -5 m 0.5 0 1 RG 0.5 w 25 -5 l S }\to q\\
\therefore\quad &q
\end{align*}
\end{document}