arXiv:2404.11624v3 Announce Type: replace-cross Abstract: We introduce Token Space, a categorical framework for AI computations based on explicit structural records. Five theses guide it: object inte...
arXiv:2606. 00220v1 Announce Type: cross Abstract: Formal methods provide rigorous accounts of program behavior, but practical software engineering often works through executable libraries, tests, and incremental design.
Programmers write formal specifications, and LLMs implement them, proving that each implementation matches its spec. Taken to its extreme, this makes specification languages the new programming langua...
arXiv:2609.23954v1 Announce Type: cross Abstract: Programmers write formal specifications, and LLMs implement them, proving that each implementation matches its spec. Taken to its extreme, this makes...
arXiv:2607. 18961v1 Announce Type: new Abstract: Large language models (LLMs) generate fluent text by incrementally predicting the next token from a prefix.
arXiv:2607. 21203v1 Announce Type: new Abstract: Description logic programs are a powerful formalism for combining rules with ontologies.
FormalEvolve is a neuro‑symbolic evolutionary search framework that treats autoformalization as a budgeted test‑time search problem. It builds a compilation‑feasible archive of formal statements and expands it using LLM‑driven mutation, crossover, bounded patch repair, and symbolic AST rewrites to generate diverse, semantically accepted formalizations. In experiments on CombiBench and ProofNet, FormalEvolve achieves higher SH@100 scores and improves theorem‑complete proving under fixed prover budgets compared to no‑archive baselines.
Description logic programs are a powerful formalism for combining rules with ontologies. The well-supported semantics for description logic programs ensures that no answer sets rely on cyclic dependencies.
arXiv:2607. 13921v1 Announce Type: cross Abstract: Languages with rich static semantics, such as Rust, provide stronger guarantees for AI-generated code, but their strictness makes generation more difficult.
arXiv:2605. 29965v2 Announce Type: replace Abstract: The development of temporal extensions of Answer Set Programming (ASP) has led to the emergence of non-monotonic linear-time (TEL), dynamic (DEL), and metric (MEL) temporal equilibrium logics.
The paper introduces TopoAlign, a framework that repurposes code repositories to train Math LLMs by decomposing code into docstrings, main functions, and dependency functions and reassembling them into structures that mirror formal mathematical statements. Using this approach, the authors train three state‑of‑the‑art models—DeepSeek‑Math, Qwen‑3, and Herald—and evaluate them on MiniF2F, Putnam, and ProofNet benchmarks. TopoAlign yields significant performance gains, notably a 17.77% improvement on BEq@10 and a 68.82% boost on typecheck@10 for DeepSeek‑Math, while also providing modest gains for Herald.
The paper introduces a differentiable evaluation engine for linear temporal logic (LTL) that is algebra‑generic and suitable for training soft‑valued systems such as neural policies and adaptive controllers. It presents an executable specification of the algebras it can accept, implements several algebras, and audits their forward and backward behavior, all within the PyTorch library telos.