  We propose Differentiable Satisfiability and Differentiable Answer Set
Programming (Differentiable SAT/ASP) for multi-model optimization. Models
(answer sets or satisfying truth assignments) are sampled using a novel SAT/ASP
solving approach which uses a gradient descent-based branching mechanism.
Sampling proceeds until the value of a user-defined multi-model cost function
reaches a given threshold. As major use cases for our approach we propose
distribution-aware model sampling and expressive yet scalable probabilistic
logic programming. As our main algorithmic approach to Differentiable SAT/ASP,
we introduce an enhancement of the state-of-the-art CDNL/CDCL algorithm for
SAT/ASP solving. Additionally, we present alternative algorithms which use an
unmodified ASP solver (Clingo/clasp) and map the optimization task to
conventional answer set optimization or use so-called propagators. We also
report on the open source software DelSAT, a recent prototype implementation of
our main algorithm, and on initial experimental results which indicate that
DelSATs performance is, when applied to the use case of probabilistic logic
inference, on par with Markov Logic Network (MLN) inference performance,
despite having advantageous properties compared to MLNs, such as the ability to
express inductive definitions and to work with probabilities as weights
directly in all cases. Our experiments also indicate that our main algorithm is
strongly superior in terms of performance compared to the presented alternative
approaches which reduce a common instance of the general problem to regular
SAT/ASP.
