Related papers: Explicit Weakening
We address the problem of translating informal mathematical proofs expressed in natural language into formal proofs in Lean4 under a constrained computational budget. Our approach is grounded in two key insights. First, informal proofs tend…
This paper describes the design and implementation of mechanisms for light-weight inclusion of formal mathematics in informal mathematical writings, particularly in a Web-based setting. This is conceptually done in three stages: (i) by…
Interpretability is essential for machine learning models to be trusted and deployed in critical domains. However, existing methods for interpreting text models are often complex, lack mathematical foundations, and their performance is not…
The challenge of delivering efficient explanations is a critical barrier that prevents the adoption of model explanations in real-world applications. Existing approaches often depend on extensive model queries for sample-level explanations…
This paper introduces a formal notion of fixed point explanations, inspired by the "why regress" principle, to assess, through recursive applications, the stability of the interplay between a model and its explainer. Fixed point…
Goedel's explicit thesis was that his undecidable formula GUS is a well-formed, well-defined formal sentence in any formalisation of Intuitive Arithmetic IA in which the axioms and rules of inference are recursively definable. His implicit…
Large language models (LLMs) have been increasingly used to interact with external environments (e.g., games, compilers, APIs) as goal-driven agents. However, it remains challenging for these language agents to quickly and efficiently learn…
The paper referred to in the title is Allard/Almgren 1981 [AA81]. Several months ago Francesco Maggi emailed me saying that the inequalities 5.3(4),(5) of \cite{AA81} were wrong. In fact, as he pointed out, their incorrectness is…
Text Simplification improves the readability of sentences through several rewriting transformations, such as lexical paraphrasing, deletion, and splitting. Current simplification systems are predominantly sequence-to-sequence models that…
An alternative form of Fermats equation[1] is proposed. It represents a portion of the identity that includes three terms of Fermats original equation. This alternative form permits an elementary and compact proof of the first case of…
The demand for accurate and efficient verification of information in texts generated by large language models (LMs) is at an all-time high, but remains unresolved. Recent efforts have focused on extracting and verifying atomic facts from…
Retrieval-Augmented Generation systems depend on retrieving semantically relevant document chunks to support accurate, grounded outputs from large language models. In structured and repetitive corpora such as regulatory filings, chunk…
This is an etude in experimental semi-rigorous (rigorizable!) mathematics. The leading asymptotics was brilliantly derived by Allan Berele and Amitai Regev for general hooks H(k,l) and general powers z, but what about more refined…
Parsing Expression Grammars (PEGs) define languages by specifying recursive-descent parser that recognises them. The PEG formalism exhibits desirable properties, such as closure under composition, built-in disambiguation, unification of…
Prior research in computational argumentation has mainly focused on scoring the quality of arguments, with less attention on explicating logical errors. In this work, we introduce four sets of explainable templates for common informal…
For many years, I have been interested in introducing students to the development of complex systems by means of modelling and refinement. To this end, I did not find anything better than presenting many examples of system developments.…
This paper shows how a recently developed view of typing as small-step abstract reduction, due to Kuan, MacQueen, and Findler, can be used to recast the development of simple type theory from a rewriting perspective. We show how standard…
This document defines extensions of the RDF data model and of the SPARQL query language that capture an alternative approach to represent statement-level metadata. While this alternative approach is backwards compatible with RDF reification…
While the task of assessing the plausibility of events such as ''news is relevant'' has been addressed by a growing body of work, less attention has been paid to capturing changes in plausibility as triggered by event modification.…
Liquid Haskell's refinement-reflection feature augments the Haskell language with theorem proving capabilities, allowing programmers to retrofit their existing code with proofs. But many of these proofs require routine, boilerplate code…