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: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.
arXiv:2510. 17944v2 Announce Type: replace-cross Abstract: In this paper, we generalize Pearl's do-calculus to an Intuitionistic setting called $j$-stable causal inference inside a topos of sheaves.
arXiv:2606. 16541v1 Announce Type: new Abstract: Autoformalization, translating natural-language mathematics into formal proof assistants, is bottlenecked not by translation fluency but by \emph{faithfulness}: a formal statement can typecheck and be provable, yet still encode a different theorem than the source intended.
arXiv:2607. 09729v1 Announce Type: new Abstract: In his 1996 doctoral thesis, Maurice Pagnucco created the first AGM-like abductive expansion operation.
arXiv:2607. 12650v1 Announce Type: cross Abstract: Tool access alone does not make LLM empirical reasoning governable: accepted outputs need not descend from attested evidence, and accepted deductions need not hold up under formal scrutiny.
arXiv:2607. 05397v1 Announce Type: cross Abstract: Agent systems increasingly execute rather than advise.
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.
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. 11252v1 Announce Type: new Abstract: Agentic AI systems routinely transport conclusions across biological, clinical and financial contexts, and the emerging safeguard is local verification: checking at each step that the entity is representable in the chosen tool, that parameters are compatible, and that outputs cohere with the plan.
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.
arXiv:2606. 31861v1 Announce Type: cross Abstract: Dynamic epistemic logic represents belief change via model transformations induced by epistemic events.
arXiv:2607. 16372v1 Announce Type: cross Abstract: Interactive theorem proving (ITP) underpins program verification and formalized mathematics, but its manual effort limits scalability.