arXiv AI By Christoph Benzm\"uller, Daniel Kirchner

First-Order Modal Logic in HOL: Deep and Shallow Embeddings with Automated Faithfulness (Extended Preprint)

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arXiv:2607. 10880v1 Announce Type: new Abstract: We extend, in Isabelle/HOL, the deep-and-shallow embedding methodology of our prior work from propositional to first-order modal logic (FML) with constant-domain Kripke semantics.

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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.