  We derive a strain-gradient theory for plasticity as the $\Gamma$-limit of
discrete dislocation fractional energies, without the introduction of a
core-radius. By using the finite horizon fractional gradient introduced by
Bellido, Cueto, and Mora-Corral of 2023, we consider a nonlocal model of
semi-discrete dislocations, in which the stored elastic energy is computed via
the fractional gradient of order $1-\alpha$. As $\alpha$ goes to $0$, we show
that suitably rescaled energies $\Gamma$-converge to the macroscopic
strain-gradient model of Garroni, Leoni, and Ponsiglione of 2010.
