Answer Set Programming Modulo Theories and Reasoning about Continuous Changes

TL;DR

This paper introduces ASPMT, a framework combining answer set programming and SMT to reason about continuous and discrete changes, enabling advanced modeling of dynamic systems.

Contribution

It presents ASPMT as a novel integration of ASP and SMT, allowing for effective reasoning about continuous changes within action languages.

Findings

ASPMT can translate tight ASP programs into SMT instances.

Enhanced C+ language handles continuous and discrete changes.

SMT solvers effectively compute ASPMT-based models.

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.