The paper introduces GUARD, a neuro‑symbolic system that autoformalizes argumentative material by completing missing premises (guards) before formal verification. It uses large language models to generate candidate guards, Isabelle/HOL to verify them, and a contrastive test to ensure the proof depends on the original premises and does not over‑generalize. Experiments on Debatepedia and ARCT show that GUARD improves verified‑faithful scores by over 30 points and reduces leakage by about 20 points compared to prior LLM‑driven theorem proving methods.
By Xin Quan, Reto Gubelmann, Andr\'e Freitas
arXiv:2607. 09729v1 Announce Type: new Abstract: In his 1996 doctoral thesis, Maurice Pagnucco created the first AGM-like abductive expansion operation.
By Ulisses Franceschi Eliano
arXiv:2608. 14004v1 Announce Type: new Abstract: In-context learning is commonly formalized as inference from examples of a function.
By Faizanuddin Ansari, Debanjan Dutta, Swagatam Das
arXiv:2605. 11644v3 Announce Type: replace-cross Abstract: Positive data can show that two tuple occurrences share a successful sentence context without certifying that they are safely interchangeable.
By Takayuki Kuriyama
We propose ZX-Calculus (Knowledge Evolution Calculus), a conservative extension of Martin-Lof Dependent Type Theory (MLTT) integrating trace-indexed types, presheaf non-monotone semantics, and constructive AGM belief revision. A Coq mechanisation accompanies the paper (34 complete proofs; zero admits for the two central results).
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...
By Christoph Benzm\"uller
arXiv:2606. 03655v1 Announce Type: new Abstract: Recent work in defeasible reasoning has seen notions of preferential semantics and entailment in the style of Kraus et al.
By Nicholas Leisegang, Thomas Meyer, Ivan Varzniczak
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.
By Christoph Benzm\"uller, Daniel Kirchner
Recent work in defeasible reasoning has seen notions of preferential semantics and entailment in the style of Kraus et al. applied to modal logics.
The paper presents three Isabelle/HOL embeddings of monadic second‑order logic (MSO): a deep embedding, a maximal‑shallow embedding, and a minimal‑shallow embedding that collapses formulas to bool. It introduces a two‑sorted substitution system that ensures capture‑avoiding substitution and proves the faithfulness of all embeddings. A fully mechanised two‑sorted downward Löwenheim‑Skolem theorem is established, showing that the minimal embedding recovers deep validity relative to countable assignments and aligns with both the general (Henkin‑style) and standard readings of MSO, while also demonstrating differences in classical MSO properties across the embeddings.
By Christoph Benzmueller, Daniel Kirchner
The paper introduces a semantic elevation operator that transforms static semantic questions about a program into dynamic questions about whether a property is preserved after the program rewrites itself. It proves that for intensional transformations the elevated property remains undecidable, showing that the class of non‑verifiable properties is closed under this operator and that repeated application climbs the arithmetical hierarchy to Υ02‑completeness. The work also demonstrates that no finite tower of verifiers can provide an unconditional certificate of preservation, and suggests a categorical perspective for future exploration.
By Jose Pascual Gumbau Mezquita
arXiv:2607. 15629v1 Announce Type: cross Abstract: Topos causal models recast causal inference inside a topos: a causal world is a presheaf, an intervention is a characteristic map into the subobject classifier, and reasoning is carried out in the intuitionistic internal language.
By Karen Sargsyan