Abstract Large Language Models perform well at natural language interpretation and reasoning, but their lack of formal correctness guarantees limits their adoption in regulated industries like finance and healthcare that operate under strict policies. To address this limitation, we launched Automated Reasoning checks (ARc) : a public service that (1) uses LLMs with optional human guidance to formalize natural language policies, allowing fine-grained control of the formalization process, and (2) uses inference-time autoformalization to validate logical correctness of natural language statements against those policies. ARc performs multiple redundant formalization steps at inference time, checking the formalizations for semantic equivalence. Our benchmarks show that ARc exceeds 99% soundness and achieves a near-zero false positive rate in identifying logical validity. Our approach produces auditable artifacts that substantiate the verification outcomes and can be used to improve the original text. ARc is the first commercial offering from a major cloud provider to integrate automated reasoning into a generative AI guardrail.

Concrete domains, especially those that allow to compare features with numeric values, have long been recognized as a very desirable extension of description logics (DLs), and significant efforts have been invested into adding them to usual DLs while keeping the complexity of reasoning in check. For expressive DLs and in the presence of general TBoxes, for standard reasoning tasks like consistency, the most general decidability results are for the so-called ω-admissible domains, which are required to be dense. Supporting non-dense domains for features that range over integers or natural numbers remained largely open, despite often being singled out as a highly desirable extension. The decidability of some extensions of ALC with non-dense domains has been shown, but existing results rely on powerful machinery that does not allow to infer any elementary bounds on the complexity of the problem. In this paper, we study an extension of ALC with a rich integer domain that allows for comparisons (between features, and between features and constants coded in unary), and prove that consistency can be solved using automata-theoretic techniques in single exponential time, and thus has no higher worst-case complexity than standard ALC. Our upper bounds apply to some extensions of DLs with concrete domains known from the literature, support general TBoxes, and allow for comparing values along paths of ordinary (not necessarily functional) roles.

We study the exact learnability of real valued graph parameters f which are known to be representable as partition functions which count the number of weighted homomorphisms into a graph H with vertex weights alpha and edge weights beta. M. Freedman, L. Lovasz and A. Schrijver have given a characterization of these graph parameters in terms of the k-connection matrices C(f,k) of f. Our model of learnability is based on D. Angluin's model of exact learning using membership and equivalence queries. Given such a graph parameter f, the learner can ask for the values of f for graphs of their choice, and they can formulate hypotheses in terms of the connection matrices C(f,k) of f. The teacher can accept the hypothesis as correct, or provide a counterexample consisting of a graph. Our main result shows that in this scenario, a very large class of partition functions, the rigid partition functions, can be learned in time polynomial in the size of H and the size of the largest counterexample in the Blum-Shub-Smale model of computation over the reals with unit cost.