Answer Set Programming Modulo Theories and Reasoning about Continuous Changes

Joohyung Lee, Yunsong Meng
7/6/2025
cs.AI

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Abstract

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.

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Cite this paper

@article{lee2025answer,
  title  = {Answer Set Programming Modulo Theories and Reasoning about Continuous Changes},
  author = {Joohyung Lee and Yunsong Meng},
  year   = {2025},
  eprint = {2507.04299},
  archivePrefix = {arXiv},
  url    = {http://arxiv.org/abs/2507.04299v1}
}

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