TeX - LaTeX Asked by user3865391 on March 13, 2021
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?
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.
Correct answer by egreg on March 13, 2021
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