Anthem 2.0: Automated Reasoning for Answer Set Programming

2025-07-15

AI Summary

This paper addresses the correctness verification of mini-gringo (a Clingo subset) logic programs. We propose a formal method based on Here-and-There (HT) logic. Our key methodological innovation is the first decidable translation of mini-gringo programs—including arithmetic constraints and choice rules—into HT formulas, enabling automated reasoning via first-order theorem provers. The approach uniformly supports three core verification tasks: (1) consistency checking between a program and a first-order specification; (2) strong equivalence checking; and (3) external equivalence checking. Experimental evaluation demonstrates that the framework effectively analyzes program tightness, ensures conformance to specifications, and precisely identifies equivalent program variants. As a result, it significantly enhances the reliability, verifiability, and maintainability of answer-set programs.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Knowledge Representation and Reasoning: Logic Programming
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty

Application Category

• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics

Abstract

Anthem 2.0 is a tool to aid in the verification of logic programs written in an expressive fragment of Clingo's input language named mini-gringo, which includes arithmetic operations and simple choice rules but not aggregates. It can translate logic programs into formula representations in the logic of here-and-there, and analyze properties of logic programs such as tightness. Most importantly, Anthem 2.0 can support program verification by invoking first-order theorem provers to confirm that a program adheres to a first-order specification, or to establish strong and external equivalence of programs. This paper serves as an overview of the system's capabilities. We demonstrate how to use Anthem 2.0 effectively and interpret its results.

Problem

• Verifies logic programs in mini-gringo fragment
• Translates programs into here-and-there logic formulas
• Supports program equivalence and specification validation

Innovation

• Translates logic programs into formula representations
• Analyzes properties like tightness in logic programs
• Invokes first-order theorem provers for verification