# Answer Set Programming Modulo Theories and Reasoning about Continuous Changes

arXiv: https://arxiv.org/abs/2507.04299 · HTML: https://mlsanity.com/paper/2507.04299/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- First posted on arXiv 6 Jul 2025.

## Abstract (arXiv)

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 SAT, ``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 ofASPMT, 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.