Related papers: The RedPRL Proof Assistant (Invited Paper)
Triangulations and higher triangulations axiomatize the calculus of derived cokernels when applied to strings of composable morphisms. While there are no cubical versions of (higher) triangulations, in this paper we use coherent diagrams to…
We introduce a proof recommender system for the HOL4 theorem prover. Our tool is built upon a transformer-based model [2] designed specifically to provide proof assistance in HOL4. The model is trained to discern theorem proving patterns…
Effective prompt engineering remains a central challenge in fully harnessing the capabilities of LLMs. While well-designed prompts can dramatically enhance performance, crafting them typically demands expert intuition and a nuanced…
Structural proof theory is praised for being a symbolic approach to reasoning and proofs, in which one can define schemas for reasoning steps and manipulate proofs as a mathematical structure. For this to be possible, proof systems must be…
For those of us who generally live in the world of syntax, semantic proof techniques such as reducibility, realizability or logical relations seem somewhat magical despite -- or perhaps due to -- their seemingly unreasonable effectiveness.…
Causal inference is at the heart of empirical research in natural and social sciences and is critical for scientific discovery and informed decision making. The gold standard in causal inference is performing randomized controlled trials;…
This paper adds to the growing literature of reinforcement learning (RL) for healthcare by proposing a novel paradigm: augmenting any predictor with Rule-based RL Layer (RRLL) that corrects the model's physiologically impossible…
We present a program for enumerating all pseudoline arrangements with a small number of pseudolines and abstract order types of small point sets. This program supports computer experiments with these structures, and it complements the…
Model-based offline Reinforcement Learning (RL) allows agents to fully utilise pre-collected datasets without requiring additional or unethical explorations. However, applying model-based offline RL to online systems presents challenges,…
Human reliability analysis (HRA) is crucial for evaluating and improving the safety of complex systems. Recent efforts have focused on estimating human error probability (HEP), but existing methods often rely heavily on expert…
This paper demonstrates how certified computational tools can be used to address various problems in control theory. In particular, we introduce PACE.jl, a Julia package that implements symbolic elimination techniques, including (among…
Enabling large language models with external tools has become a pivotal strategy for extending their functionality beyond text space. To enhance LLMs' tool-calling abilities, previous approaches primarily rely on supervised fine-tuning…
This report describes three particular technological advances in formal proofs. The HOL Light proof assistant will be used to illustrate the design of a highly reliable system. Today, proof assistants can verify large bodies of advanced…
This paper describes Hipster, a system integrating theory exploration with the proof assistant Isabelle/HOL. Theory exploration is a technique for automatically discovering new interesting lemmas in a given theory development. Hipster can…
This paper introduces a uniform substitution calculus for differential refinement logic dRL. The logic dRL extends the differential dynamic logic dL such that one can simultaneously reason about properties of and relations between hybrid…
Research Replication Prediction (RRP) is the task of predicting whether a published research result can be replicated or not. Building an interpretable neural text classifier for RRP promotes the understanding of why a research paper is…
We contribute XTT, a cubical reconstruction of Observational Type Theory which extends Martin-L\"of's intensional type theory with a dependent equality type that enjoys function extensionality and a judgmental version of the unicity of…
A reliable modeling of uncertain evidence in Bayesian networks based on a set-valued quantification is proposed. Both soft and virtual evidences are considered. We show that evidence propagation in this setup can be reduced to standard…
Existing datasets for multimodal table understanding, such as MMTab, primarily provide short factual answers without explicit multi-step reasoning supervision. Models trained on these datasets often generate brief responses that offers…
We propose a synthesis of the two proof styles of interactive theorem proving: the procedural style (where proofs are scripts of commands, like in Coq) and the declarative style (where proofs are texts in a controlled natural language, like…