  A more complete understanding of entanglement entropy in a covariant manner
could inform the search for quantum gravity. We build on work in this direction
by extending previous results to disjoint regions in $1+1$D. We investigate the
entanglement entropy of a scalar field in disjoint intervals within the causal
set framework, using the spacetime commutator and correlator,
$i\mathbf{\Delta}$ and $\mathbf{W}$ (or the Pauli-Jordan and Wightman
functions), respectively. A new truncation scheme for disjoint causal diamonds
is presented, which follows from the single diamond truncation scheme. We
investigate setups including two and three disjoint causal diamonds, as well as
a single causal diamond that shares a boundary with a larger global causal
diamond. In all the cases that we study, our results agree with the expected
area laws. In addition, we study the mutual information in the two disjoint
diamonds setup. The ease of our calculations indicate our methods to be a
useful tool for numerically studying such systems. We end with a discussion of
some of the strengths and future applications of the spacetime formulation we
use in our entanglement entropy computations, both in causal set theory and in
the continuum.
