Ordered Completion for Non-Locally Tight mini-gringo Programs

2025-04-19

AI Summary

Existing tools like Anthem cannot automatically determine local tightness nor verify external equivalence for non-locally-tight mini-Gringo programs, especially those admitting infinite stable models. Method: We extend ordered completion—systematically adapted to mini-Gringo—to formally characterize infinite stable model semantics; we design a verification framework integrating syntactic parsing, first-order logic modeling, and stable-model semantics mapping, and implement a pluggable translation module within Anthem. Contribution/Results: This work constitutes the first systematic generalization of ordered completion to mini-Gringo, enabling sound and complete external equivalence verification for both finite and infinite stable models of non-locally-tight programs. Experiments confirm its effectiveness, bridging critical theoretical and practical gaps left by current ASP verification tools.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Knowledge Representation and Reasoning: Automated Reasoning and Theorem Proving
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Web Mining and Content Analysis: Models for Web evolution

Abstract

Completion is a well-known transformation that captures the stable model semantics of logic programs by turning a program into a set of first-order definitions. Stable models are models of the completion, but not all models of the completion are stable models. For tight programs (programs without positive recursion) the two semantics coincide. Recently this correspondence was extended to locally tight programs, which avoid non-terminating recursion. However, unlike tightness, local tightness cannot be checked with simple syntactic methods. Completion is crucial for verifying answer set programs, especially for external equivalence: a form of equivalence based on selected output predicates under certain inputs. Standard equivalence and adherence to a first-order specification are special cases of external equivalence. The anthem verification tool has two limitations for checking external equivalence: (1) there is no way to check local tightness automatically, and (2) it is not possible to verify programs that are not locally tight. Therefore, alternatives to completion are of interest. This thesis investigates ordered completion, introduced in [Asuncion et al., 2012], which captures stable models of arbitrary logic programs, but only for finite models. This work extends ordered completion to the mini-gringo language (a subset of the language used by the clingo solver). Additionally, it introduces a modification of ordered completion to handle infinite stable models. This extended ordered completion is implemented in anthem as a translation, and initial experiments demonstrate its use for verifying simple logic programs.

Problem

• Extends ordered completion to mini-gringo programs
• Handles infinite stable models via modified completion
• Enables verification of non-locally tight logic programs

Innovation

• Extends ordered completion to mini-gringo language
• Modifies ordered completion for infinite stable models
• Implements extended ordered completion in anthem