First-Order Modal Logic in HOL: Deep and Shallow Embeddings with Automated Faithfulness (Extended Preprint)
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. Three embeddings of FML into classical higher-order logic (HOL) are provided side by side: a deep embedding, a heavyweight maximal-shallow embedding, and a lightweight minimal-shallow embedding. The minimal-shallow embedding is presented as an Isabelle/HOL locale, parametrised by an accessibility relation, a world-indexed interpretation, a universe of worlds, and a variable assignment; the locale form admits a global faithfulness theorem, stating that quantifying over all minimal-shallow interpretations recovers...
| Authors | Christoph Benzmüller, Daniel Kirchner |
|---|---|
| Primary category | cs.AI |
| Published | 12 July 2026 |
| Last updated at source | 17 July 2026 |
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