Related papers: A Novice-Friendly Induction Tactic for Lean
The motivation for this paper comes out of our experience with teaching natural deduction (ND) and with the way this formal system is implemented by the \textsc{Coq} proof assistant, namely by means of so-called tactics, which are…
Induction in saturation-based first-order theorem proving is a new exciting direction in the automation of inductive reasoning. In this paper we survey our work on integrating induction directly into the saturation-based proof search…
Combining a pretrained language model (PLM) with textual patterns has been shown to help in both zero- and few-shot settings. For zero-shot performance, it makes sense to design patterns that closely resemble the text seen during…
Recent progress in formal theorem proving has benefited from large-scale proof generation and verifier-aware training, but agentic proving is rarely integrated into prover training, appearing only at inference time. We present OProver, a…
Large language model (LLM) development is currently driven by large-scale empirical iteration over data mixtures, reward models, routing strategies, and evaluation pipelines. Here, we argue that many central questions in LLM development and…
We scale layered modal type theory to dependent types, introducing DeLaM, dependent layered modal type theory. This type theory is novel in that we have one uniform type theory in which we can not only compose and execute code, but also…
Large Language Models (LLMs) are reported to hold undesirable attestation bias on inference tasks: when asked to predict if a premise P entails a hypothesis H, instead of considering H's conditional truthfulness entailed by P, LLMs tend to…
Formalized mathematics has recently garnered significant attention for its ability to assist mathematicians across various fields. Premise retrieval, as a common step in mathematical formalization, has been a challenge, particularly for…
In this paper we present a formalization of Intuitionistic Propositional Logic in the Lean proof assistant. Our approach focuses on verifying two completeness proofs for the studied logical system, as well as exploring the relation between…
Recent approaches have explored language-guided classifiers capable of classifying examples from novel tasks when provided with task-specific natural language explanations, instructions or prompts (Sanh et al., 2022; R. Menon et al., 2022).…
A popular method to adapt large language models (LLMs) to new tasks is in-context learning (ICL), which is effective but incurs high inference costs as context length grows. In this paper we propose a method to perform instruction…
Mathematical induction is a fundamental tool in computer science and mathematics. Henkin initiated the study of formalization of mathematical induction restricted to the setting when the base case B is set to singleton set containing 0 and…
Although Large Language Models (LLMs) are showing impressive performance on a wide range of Natural Language Processing tasks, researchers have found that they still have limited ability to conduct induction. Recent works mainly adopt…
Optimising deep learning inference across edge devices and optimisation targets such as inference time, memory footprint and power consumption is a key challenge due to the ubiquity of neural networks. Today, production deep learning…
Recent embedding-based methods in unsupervised bilingual lexicon induction have shown good results, but generally have not leveraged orthographic (spelling) information, which can be helpful for pairs of related languages. This work…
Performing inference on large volumes of samples with large language models (LLMs) can be computationally and financially costly in industry and real-world use. We propose batch prompting, a simple yet effective prompting approach that…
In this paper, we introduce a system called GamePad that can be used to explore the application of machine learning methods to theorem proving in the Coq proof assistant. Interactive theorem provers such as Coq enable users to construct…
We advocate here the use of computational logic for systems biology, as a \emph{unified and safe} framework well suited for both modeling the dynamic behaviour of biological systems, expressing properties of them, and verifying these…
We define a general class of dependent type theories, encompassing Martin-L\"of's intuitionistic type theories and variants and extensions. The primary aim is pragmatic: to unify and organise their study, allowing results and constructions…
To enhance reasoning capabilities, previous works have explored incorporating special-purpose tokens into the training process. These strategies strengthen the learning mechanism of transformer-based large language models (LLMs). Building…