Is it safe to temporarily redefine \and, \or, and \not?

Question

I'm writing lots of logic expressions in LaTeX and I'd much rather write $p \and \not q \or r$ than $p \land \lnot q \lor r$. I was thinking of doing something like this:

\newenvironment{logic}{%
\renewcommand\and\land%
\renewcommand\or\lor%
\renewcommand\not\lnot%
}{}

Then I could simply

\begin{logic}
    p \and \not q \or r
\end{logic}

Are the commands \and, \or, and \not built into TeX? Is it safe to temporarily redefine them? If not, can you recommend any alternatives? Thanks!

Answer 1

They are not built into TeX (which is called primitive in TeX). For example, \and is defined by latex as \end {tabular}\hskip 1em \@plus .17fil\begin {tabular}[t]{c}. However \or, unlike \and and \not, is not a macro but a TeX primitive. It is not a good idea to redefine it.

I think you do can overwrite them if you like as long as you enclose them within in a group, or you won't use their original meaning. For example, you are not likely to use \and after \author in most cases.

Answer 2

The macros \and and \not are predefined in LaTeX, but the former is generally used in the \author{} command to separate authors, while the latter is used (generally) to form the negation of already-existing symbols, as in \not\perp (not orthogonal).

The MWE below uses the \xspace macro to automate good spacing following the redefined commands in non-math mode.

\documentclass{article}
\usepackage{xspace}
\newenvironment{logic}
   {\renewcommand{\and}{\ensuremath{\land}\xspace}
    \renewcommand{\or}{\ensuremath{\lor}\xspace}
    \renewcommand{\not}{\ensuremath{\lnot}}}
   {}     
\begin{document}
\begin{logic}
$p$ \and \not $q$ \or $r$ 
\end{logic}
\end{document}