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).

In addition, we illustrate the potential of ASP including molecular biology (Gebser et computational hardness of our application problem al. 2010a, 2010b), decision support system for space by explaining its connection to the NPcomplete shuttle controllers (Balduccini, Gelfond, and decision problem Exact-3-SAT.

We propose a declarative framework for representing and reasoning about truthfulness of agents using answer set programming. We show how statements by agents can be evaluated against a set of observations over time equipped with our knowledge about the actions of the agents and the normal behavior of agents. We illustrate the framework using examples and discuss possible extensions that need to be considered.

We propose a declarative framework for representing and reasoning about truthfulness  of agents using answer set programming. We show how statements by agents can be  evaluated against a set of observations over time equipped with our knowledge about  the actions of the agents and the normal behavior of agents. We illustrate the framework  using examples and discuss possible extensions that need to be considered.