Related papers: Algebraic Foundations of Proof Refinement
Refinement types -- types qualified with logical predicates -- have proven effective for lightweight verification in languages like Liquid Haskell, F*, and Dafny. However, in these systems refinements are either written in a separate…
We consider the challenging problem of using domain knowledge to improve deep reinforcement learning policies. To this end, we propose LEGIBLE, a novel approach, following a multi-step process, which starts by mining rules from a deep RL…
Dependencies have played a significant role in database design for many years. They have also been shown to be useful in query optimization. In this paper, we discuss dependencies between lexicographically ordered sets of tuples. We…
Reasoning language models can solve increasingly complex tasks, but struggle to produce the calibrated confidence estimates necessary for reliable deployment. Existing calibration methods usually depend on labels or repeated sampling at…
In this paper we extend the research programme in algebraic proof theory from axiomatic extensions of the full Lambek calculus to logics algebraically captured by certain varieties of normal lattice expansions (normal LE-logics).…
Formally verifying properties of software code has been a highly desirable task, especially with the emergence of LLM-generated code. In the same vein, they provide an interesting avenue for the exploration of formal verification and…
Agent-compiled knowledge bases provide persistent external knowledge for large language model (LLM) agents in open-ended, knowledge-intensive downstream tasks. Yet their quality is systematically limited by \emph{incompleteness},…
To take advantage of Large Language Model in theorem formalization and proof, we propose a reinforcement learning framework to iteratively optimize the pretrained LLM by rolling out next tactics and comparing them with the expected ones.…
In this paper we demonstrate that $\textit{context free grammar (CFG) based methods for grammar induction benefit from modeling lexical dependencies}$. This contrasts to the most popular current methods for grammar induction, which focus on…
Fine-tuning LLMs for classification typically maps inputs directly to labels. We ask whether attaching brief explanations to each label during fine-tuning yields better models. We evaluate conversational response quality along three axes:…
Identifying control-friendly models of nonlinear systems remains one of the major challenges at the intersection of system identification and control. The Linear Parameter-Varying (LPV) framework offers a promising solution, but existing…
Deploying machine learning models in safety-related do-mains (e.g. autonomous driving, medical diagnosis) demands for approaches that are explainable, robust against adversarial attacks and aware of the model uncertainty. Recent deep…
In various provers and deductive verification tools, logical transformations are used extensively in order to reduce a proof task into a number of simpler tasks. Logical transformations are often part of the trusted base of such tools. In…
In environments with sparse or delayed rewards, reinforcement learning (RL) incurs high sample complexity due to the large number of interactions needed for learning. This limitation has motivated the use of large language models (LLMs) for…
Software is now ubiquitous and involved in complex interactions with the human users and the physical world in so-called cyber-physical systems where the management of time is a major issue. Separation of concerns is a key asset in the…
The $Reflection$ $Calculus$ ($\mathcal{\mathbf{RC}}$) is the fragment of the polymodal logic $\mathcal{\mathbf{GLP}}$ in the language $L^+$ whose formulas are built up from $\top$ and propositional variables using conjunction and diamond…
This is the second in a series of papers extending Martin-L\"{o}f's meaning explanation of dependent type theory to account for higher-dimensional types. We build on the cubical realizability framework for simple types developed in Part I,…
As a pivotal component to attaining generalizable solutions in human intelligence, reasoning provides great potential for reinforcement learning (RL) agents' generalization towards varied goals by summarizing part-to-whole arguments and…
Interpretable rationales for model predictions are crucial in practical applications. We develop neural models that possess an interpretable inference process for dependency parsing. Our models adopt instance-based inference, where…
The convergence of deep learning and formal mathematics has spurred research in formal verification. Statement autoformalization, a crucial first step in this process, aims to translate informal descriptions into machine-verifiable…