  This paper describes diff-SAT, an Answer Set and SAT solver which combines
regular solving with the capability to use probabilistic clauses, facts and
rules, and to sample an optimal world-view (multiset of satisfying Boolean
variable assignments or answer sets) subject to user-provided probabilistic
constraints. The sampling process minimizes a user-defined differentiable
objective function using a gradient descent based optimization method called
Differentiable Satisfiability Solving ($\partial\mathrm{SAT}$) respectively
Differentiable Answer Set Programming ($\partial\mathrm{ASP}$). Use cases are
i.a. probabilistic logic programming (in form of Probabilistic Answer Set
Programming), Probabilistic Boolean Satisfiability solving (PSAT), and
distribution-aware sampling of model multisets (answer sets or Boolean
interpretations).
