# Notation for joins/meets in a lattice

Most often I see \$\lor\$ and \$\land\$ used for the join and meet operations respectively in a lattice, however what I am writing makes concurrent use of both symbolic logic and a particular lattice, thus I am already using these operations to express logical conjunction/disjunction and am unsure what to use for the joins/meets. For example I don't want to use \$\cup\$ and \$\cap\$ since I think this might cause confusion with sets or enable some unconscious error where I treat them like their set counter parts i.e. I might accidentally distribute them over each other despite not dealing with a distributive lattice, likewise for similar reasons I'd rather not use \$\sqcup\$ and \$\sqcap\$ as I often use the latter for 'disjoint' unions or coproducts. So with all of that in mind what are some standard alternatives to these that I could use for joins/meets in a lattice?

• There are \curlyvee and \curlywedge in amssymb. Dec 7, 2020 at 22:43

You shouldn't be using \lor and \land for operations in a lattice. There are semantically better names

\vee \wedge

and reserve \lor and \land to formal logic formulas. By the way, “vee” and “wedge” are common names for the operations in lattices.

Yes, they normally point to the same symbol and indeed, the LaTeX kernel does

\DeclareMathSymbol{\wedge}{\mathbin}{symbols}{"5E}
\DeclareMathSymbol{\vee}{\mathbin}{symbols}{"5F}
\DeclareMathSymbol{\land}{\mathbin}{symbols}{"5E}
\DeclareMathSymbol{\lor}{\mathbin}{symbols}{"5F}

However, using semantically sounder names allows you to change the representation of the symbols for lattices by just redefining \vee and \wedge.

For instance, you could use \curlyvee and \curlywedge from amssymb:

\usepackage{amssymb}

and then

\renewcommand{\vee}{\curlyvee}
\renewcommand{\wedge}{\curlywedge}

so, if you later change your mind, you can always remove the redefinitions or adopt different ones.

You could adopt the names \join and \meet, if you so prefer:

\newcommand{\join}{\curlyvee}
\newcommand{\meet}{\curlywedge}

but the idea is the same.