arXiv:2607. 21199v1 Announce Type: cross 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.
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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.
The paper introduces a new calculus that integrates ground instantiations, CDCL(T)-style rules, and non‑ground conflict analysis for SMT solving. By performing resolution on the original non‑ground clauses, the solver learns more general, often non‑redundant clauses, potentially yielding exponentially shorter proofs. The approach also incorporates chronological backtracking and is shown to simulate several existing solving frameworks, including CDCL, SCL(FOL), SCL(T), and Resolution.
arXiv:2607. 13069v1 Announce Type: new Abstract: Large language models produce chain-of-thought (CoT) reasoning that appears logically sound yet may not genuinely depend on its stated premises.
arXiv:2608. 09190v1 Announce Type: new Abstract: GK is a query-directed first-order prover that extends ordinary resolution-based proof search with explicit positive and negative claims, numerical confidence values, and prioritized default rules with exceptions.
arXiv:2608. 19009v2 Announce Type: replace Abstract: Large language models (LLMs) are increasingly paired with verifiers (step checkers, self-consistency filters, tool-based fact checkers, formal proof assistants) that claim to detect the model's errors.
arXiv:2606. 00671v1 Announce Type: new Abstract: We present AXIOM, a trust-first neuro-symbolic execution architecture for natural-language mathematical reasoning.