Answer Set Programming Modulo Theories and Reasoning about Continuous Changes

2025-07-06

AI Summary

This work addresses the challenge of unifying discrete and continuous dynamic systems within a single declarative modeling framework. We propose ASPMT—a novel integration of Answer Set Programming (ASP) and Satisfiability Modulo Theories (SMT)—which extends action language C+ to support continuous variables and cumulative effects. Methodologically, ASPMT redefines the semantics of C+ using functional stable models, enabling tight coupling between ASP’s nonmonotonic reasoning and SMT’s expressive theory reasoning over continuous domains. It explicitly formalizes sustained actions’ cumulative impact on continuous resources (e.g., energy, time). Furthermore, ASPMT provides an automated translation from high-level ASPMT programs into quantifier-free SMT instances, solvable by off-the-shelf SMT solvers. Experimental evaluation demonstrates that ASPMT retains the expressiveness of declarative action languages while ensuring computational tractability for reasoning tasks involving continuous change—thereby bridging a key gap between symbolic AI and hybrid dynamical systems modeling.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Knowledge Representation and Reasoning: Action, Change, and Causality
• Planning, Routing, and Scheduling: Mixed Discrete/Continuous Planning

Application Category

• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

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.

Problem

• Integrating ASP and SMT for continuous and discrete reasoning
• Enhancing action language C+ to handle continuous changes
• Reformulating C+ semantics using ASPMT for SMT solvers

Innovation

• Integrates ASP and SMT for continuous changes
• Translates tight ASPMT programs to SMT
• Enhances action language C+ with ASPMT