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Complex automated proof strategies are often difficult to extract, visualise, modify, and debug. Traditional tactic languages, often based on stack-based goal propagation, make it easy to write proofs that obscure the flow of goals between…

Although automated reasoning with diagrams has been possible for some years, tools for diagrammatic reasoning are generally much less sophisticated than their sentential cousins. The tasks of exploring levels of automation and abstraction…

We introduce Tinker, a tool for designing and evaluating proof strategies based on proof-strategy graphs, a formalism previously introduced by the authors. We represent proof strategies as open-graphs, which are directed graphs with…

Formally verifying the correctness of mathematical proofs is more accessible than ever, however, the learning curve remains steep for many of the state-of-the-art interactive theorem provers (ITP). Deriving the most appropriate subsequent…

LLM-generated explanations can make technical content more accessible, but there is a ceiling on what they can support interactively. Because LLM outputs are static text, they cannot be executed or stepped through. We argue that grounding…

Enabling more concise and modular proofs is essential for advancing formal reasoning using interactive theorem provers (ITPs). Since many ITPs, such as Rocq and Lean, use tactic-style proofs, learning higher-level custom tactics is crucial…

Many problems, especially those with a composite structure, can naturally be expressed in higher order logic. From a KR perspective modeling these problems in an intuitive way is a challenging task. In this paper we study the graph mining…

We present Proof-of-Perception (PoP), a tool-using framework that casts multimodal reasoning as an executable graph with explicit reliability guarantees. Each perception or logic node outputs a conformal set, yielding calibrated, stepwise…

This is the full version of a paper submitted to the Computability in Europe (CiE 2023) conference, with all proofs omitted there. In 2012 P. D. Azar and S. Micali introduced a new model of interactive proofs, called "Rational Interactive…

Motivated by the transfer of proofs between proof systems, and in particular from first order automated theorem provers (ATPs) to interactive theorem provers (ITPs), we specify an extension of the TPTP derivation text format to describe…

The growing demand for automated graph algorithm reasoning has attracted increasing attention in the large language model (LLM) community. Recent LLM-based graph reasoning methods typically decouple task descriptions from graph data,…

Machine-assisted theorem proving refers to the process of conducting structured reasoning to automatically generate proofs for mathematical theorems. Recently, there has been a surge of interest in using machine learning models in…

Researchers have relegated natural language processing tasks to Transformer-type models, particularly generative models, because these models exhibit high versatility when performing generation and classification tasks. As the size of these…

One important approach to software verification is interactive theorem proving. However, writing formal proofs often requires substantial human effort, making proof automation highly important. Traditionally, proof automation has relied on…

String diagrams are an increasingly popular algebraic language for the analysis of graphical models of computations across different research fields. Whereas string diagrams have been thoroughly studied as semantic structures, much less…

A number of flexible tactic-based logical frameworks are nowadays available that can implement a wide range of mathematical theories using a common higher-order metalanguage. Used as proof assistants, one of the advantages of such powerful…

One of the most attractive features of untyped languages is the flexibility in term creation and manipulation. However, with such power comes the responsibility of ensuring the correctness of these operations. A solution is adding run-time…

The distributed representations currently used are dense and uninterpretable, leading to interpretations that themselves are relative, overcomplete, and hard to interpret. We propose a method that transforms these word vectors into reduced…

Reasoning methods such as chain-of-thought prompting and self-consistency have shown immense potential to improve the accuracy of large language models across various reasoning tasks. However such methods involve generation of lengthy…

Although most of the automated theorem-proving approaches depend on formal proof systems, informal theorem proving can align better with large language models' (LLMs) strength in natural language processing. In this work, we identify a…