Towards a Certifying Grounder

2026-07-23

AI Summary

This work addresses the trust gap between high-level specifications and low-level inputs in declarative solving, which arises from unverified grounding steps. To bridge this gap, the paper presents CertiFOX, the first certifiable grounding framework. CertiFOX introduces a Grounding Normal Form (GNF) as an intermediate representation and features a certifying grounder, GroundFOX, which produces grounded programs accompanied by formal proofs of correctness. An independent verifier, CheckFOX, is provided to efficiently validate the logical equivalence between the original specification and the grounded output. Experimental results demonstrate that GroundFOX achieves performance comparable to state-of-the-art grounders, while CheckFOX incurs verification overhead that is only a small constant factor of the grounding time, confirming the feasibility and practicality of the proposed approach.

Abstract

Grounding, the translation of high-level theories into equivalent quantifier-free formulas, is a crucial step in declarative solving, yet it has so far escaped the proof-logging revolution. When this grounding step is not certifying, there is no way of knowing that the obtained solutions actually correspond to the original problem specification, resulting in a trust gap. In this paper, we close the trust gap between the user's high-level specification and the solver's low-level input by introducing a novel certifying grounding framework for first-order logic model expansion (FOX) over finite domains. We present CertiFOX, a framework consisting of: (1) a proof format for grounding derivations, (2) GroundFOX, a certifying grounder operating on theories in Grounding Normal Form (GNF)--a new normal form designed for compact, domain-aware grounding--and (3) CheckFOX, an independent proof checker. Our approach guarantees that the grounder's output is equivalent to the input specification, setting the stage for trustworthy end-to-end certified solving pipelines for declarative languages. Experimental evaluation confirms that CertiFOX is a feasible approach. The GroundFOX grounder is broadly comparable with other grounders, and proof checking with CheckFOX adds overhead within a small constant factor of grounding time.

Problem

• grounding
• certifying
• declarative solving
• trust gap
• first-order logic

Innovation

• certifying grounding
• Grounding Normal Form
• proof checking
• first-order logic model expansion
• declarative solving