arXiv:2606. 14688v1 Announce Type: cross Abstract: AI systems coupled to proof assistants now generate formal mathematics at scale, and the gap between what a checker can verify and what a mathematician would value has become the binding constraint.
By Xiaoyu Li, Andi Han, Dai Shi, Zheng Gao, Jiaojiao Jiang, Junbin Gao
arXiv:2608. 15147v1 Announce Type: new Abstract: Machine intelligence has conquered the symbolic world but stalled at the physical one.
By Jiang Jiang (Persagy Science and Technology Co., Beijing, China), Yifu Sun (Persagy Science and Technology Co., Beijing, China), Qi Shen (Persagy Science and Technology Co., Beijing, China)
arXiv:2601. 18747v2 Announce Type: replace-cross Abstract: Modern AI agents increasingly rely on search infrastructure to execute complex, neuro-symbolic reasoning workflows.
By Amir Aavani
arXiv:2303. 04203v4 Announce Type: replace Abstract: The theory of computation was built to answer Turing's question: what is effectively calculable by an unbounded, immortal, disembodied agent following rules?
By Xin Li
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
The paper introduces a hierarchy of four increasingly strict faithfulness criteria—discrimination, logical admissibility, monotonic logical faithfulness, and probabilistic logical faithfulness—for evaluating knowledge base completion models, particularly when the target is a description logic knowledge base. It demonstrates that ranking accuracy alone does not guarantee logical faithfulness and shows that current embedding models fail to satisfy any of the criteria across the hierarchy. The authors provide a formal grounding for the strongest criterion using relative model counts and evaluate several models on εL ontologies, revealing gaps between performance metrics and logical correctness.
By Olga Mashkova, Robert Hoehndorf