  In this paper, we investigate the effects of stochastic resetting on
diffusion in $\R^d\backslash \calU$, where $\calU$ is a bounded obstacle with a
partially absorbing surface $\partial \calU$. We begin by considering a Robin
boundary condition with a constant reactivity $\kappa_0$, and show how previous
results are recovered in the limits $\kappa_0\rightarrow 0,\infty$. We then
generalize the Robin boundary condition to a more general probabilistic model
of diffusion-mediated surface reactions using an encounter-based approach. The
latter considers the joint probability density or propagator
$P(\x,\ell,t|\x_0)$ for the pair $(\X_t,\ell_t)$ in the case of a perfectly
reflecting surface, where $\X_t$ and $\ell_t$ denote the particle position and
local time, respectively. The local time determines the amount of time that a
Brownian particle spends in a neighborhood of the boundary. The effects of
surface reactions are then incorporated via an appropriate stopping condition
for the boundary local time. We construct the boundary value problem (BVP)
satisfied by the propagator in the presence of resetting, and use this to
derive implicit equations for the marginal density of particle position and the
survival probability. We highlight the fact that these equations are difficult
to solve in the case of non-constant reactivities, since resetting is not
governed by a renewal process. We then consider a simpler problem in which both
the position and local time are reset. In this case, the survival probability
with resetting can be expressed in terms of the survival probability without
resetting, which allows us to explore the dependence of the MFPT on the
resetting rate $r$ and the type of surface reactions. The theory is illustrated
using the example of a spherically symmetric surface.
