Answer Set Programming Modulo Theories and Reasoning about Continuous Changes

Answer Set Programming Modulo Theories (ASPMT) is a new framework of tight integration of answer set programming (ASP) and satisfiability modulo theories (SMT). Similar to the relationship between first-order logic and SMT, it is based on a recent proposal of the functional stable model semantics by fixing interpretations of background theories. Analogously to a known relationship between ASP and SA T, "tight" ASPMT programs can be translated into SMT instances. We demonstrate the usefulness of ASPMT by enhancing action language C + to handle continuous changes as well as discrete changes. We reformulate the semantics of C + in terms of ASPMT, and show that SMT solvers can be used to compute the language. We also show how the language can represent cumulative effects on continuous resources.