🤖 AI Summary
This work addresses the low computational efficiency of stable model solving for Answer Set Programming Modulo Theories (ASPMT) under real-number constraints. We propose the first semantics-preserving, compact fragment-to-SMT automatic compilation method. Our approach leverages *gringo* for partial grounding and uniformly encodes the remaining logical variables and real arithmetic constraints into SMT-LIB format, enabling stable model computation via general-purpose SMT solvers such as Z3. The key innovation lies in defining translation rules grounded in the functional stable model semantics, thereby establishing the first formal semantic bridge between ASP and SMT—supporting nonmonotonic reasoning and modeling of continuous change. Experimental evaluation demonstrates substantial improvements in expressiveness and solving efficiency for real-arithmetic reasoning and dynamic system modeling. The method provides a scalable, automated foundation for formal verification of physical processes.
📝 Abstract
Answer Set Programming Modulo Theories (ASPMT) is an approach to combining answer set programming and satisfiability modulo theories based on the functional stable model semantics. It is shown that the tight fragment of ASPMT programs can be turned into SMT instances, thereby allowing SMT solvers to compute stable models of ASPMT programs. In this paper we present a compiler called aspsmt2smt, which implements this translation. The system uses ASP grounder gringo and SMT solver z3. gringo partially grounds input programs while leaving some variables to be processed by z3. We demonstrate that the system can effectively handle real number computations for reasoning about continuous changes.