Linear diagrams have recently been shown to be
more effective than Euler diagrams when used
for set-based reasoning. However, unlike the
growing corpus of knowledge about formal aspects
of Euler and Venn diagrams, there has been no
formalisation of linear diagrams. To fill this
knowledge gap, we present and formalise Point
and Line (PaL) diagrams, an extension of simple
linear diagrams containing points, thus providing
a formal foundation for an effective visual
language.We prove that PaL diagrams are exactly
as expressive as monadic first-order logic with
equality, gaining, as a corollary, an equivalence
with the Euler diagram extension called spider
diagrams. The method of proof provides translations
between PaL diagrams and sentences of monadic
first-order logic
