arXiv AI
Mathematical Proof Assistants for Teaching Logic: The LogiKEy Methodology
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Oct 6
Mathematical Proof Assistants for Teaching Logic: The LogiKEy Methodology
We report on an approach to teaching logic to mixed groups of computer science, mathematics, and philosophy students, based on the logico-pluralistic LogiKEy methodology, used for more than a decade i...
arXiv AI
Sep 30
Proofs Without Nominals: G\"odel's Ontological Argument, its Shallow Embedding, and the Open Questions of the Monatshefte Notes
arXiv:2609.36279v1 Announce Type: cross Abstract: The shallow embedding of higher-order modal logic in classical higher-order logic, used in Benzm\"uller and Scott's Notes on G\"odel's and Scott's va...
arXiv AI
Jun 30
LAMP: Lean-based Agentic framework with MCP and Proof Repair
arXiv:2606. 28841v1 Announce Type: cross Abstract: Large language models are increasingly capable of mathematical reasoning, but the proofs they generate are often unreliable and hard to verify.
arXiv AI
Sep 24
G\"odel's and Scott's Variants of the Ontological Argument in Lean 4
This paper reports a full, structure‑preserving port of the Isabelle/HOL dataset on G"odel’s and Scott’s modal ontological arguments to Lean 4. The port consists of 30 Lean 4 modules that mirror the original theories in section structure, declaration order, and naming, and a comparison tool confirms that all 548 statements are identical. The Lean 4 development reproduces every proof from the Isabelle/HOL version—including the inconsistency of G"odel’s 1970 axioms, the repaired variants, Scott’s variant, modal collapse, monotheism, and the ultrafilter property—while also proving five previously unproven statements and documenting the remaining 45 as unresolved. "whyItMatters":"The work demonstrates that Lean 4 can faithfully replicate a complex formal development from Isabelle/HOL, providing a new, lean‑based foundation for further exploration of modal ontological arguments."
arXiv AI
Sep 28
G\"odel's and Scott's Variants of the Ontological Argument in Lean 4 and TPTP THF
arXiv:2609.26806v2 Announce Type: replace-cross Abstract: This paper presents a complete, structure-preserving port to Lean 4 of the Isabelle/HOL dataset accompanying Benzm\"uller and Scott's study o...
arXiv AI
Jun 15
MA-ProofBench: A Two-Tiered Evaluation of LLMs for Theorem Proving in Mathematical Analysis
arXiv:2606. 13782v1 Announce Type: new Abstract: Large Language Models (LLMs) have made notable progress in automated theorem proving, yet existing formal benchmarks remain limited in both mathematical coverage and difficulty.