Related papers: Natural Language Proof Checking in Introduction to…

In order to help students learn how to write mathematical proofs, we adapt the Coq proof assistant into an educational tool we call Waterproof. Like with other interactive theorem provers, students write out their proofs inside the software…

Scientific argumentation is a core science and engineering practice and a necessary 21st Century workforce skill. Due to the nature of large enrollment classes, it is difficult to individually assess students and provide feedback on their…

Proof competence, i.e. the ability to write and check (mathematical) proofs, is an important skill in Computer Science, but for many students it represents a difficult challenge. The main issues are the correct use of formal language and…

Research in natural language processing proceeds, in part, by demonstrating that new models achieve superior performance (e.g., accuracy) on held-out test data, compared to previous results. In this paper, we demonstrate that test-set…

We present a comprehensive programme analysing the decomposition of proof systems for non-classical logics into proof systems for other logics, especially classical logic, using an algebra of constraints. That is, one recovers a proof…

Introductory programming courses often emphasize mastering syntax and basic constructs before progressing to more complex and interesting programs. This bottom-up approach can be frustrating for novices, shifting the focus away from problem…

We propose an algorithm that test membership for regular expressions and show that the algorithm is correct. This algorithm is written in the style of a sequent proof system. The advantage of this algorithm over traditional ones is that the…

Natural language inference (NLI) is a fundamental NLP task, investigating the entailment relationship between two texts. Popular NLI datasets present the task at sentence-level. While adequate for testing semantic representations, they fall…

Writing a good essay typically involves students revising an initial paper draft after receiving feedback. We present eRevise, a web-based writing and revising environment that uses natural language processing features generated for…

Proust is a small Racket program offering rudimentary interactive assistance in the development of verified proofs for propositional and predicate logic. It is constructed in stages, some of which are done by students before using it to…

As humans, we often rely on language to learn language. For example, when corrected in a conversation, we may learn from that correction, over time improving our language fluency. Inspired by this observation, we propose a learning…

The purpose of this paper is to give an easy to understand with step-by-step explanation to allow interested people to fully appreciate the power of natural deduction for first-order logic. Natural deduction as a proof system can be used to…

In the paper I discuss a tool for helping students in their symbolizations of natural language sentences using the formal language of classical first order logic (CFOL). The tool is an extension of Hintikka's concept of (Inquirer's) range…

We discuss two proof evaluation activities meant to promote the acquisition of learning behaviors of professional mathematics within an introductory undergraduate proof-writing course. These learning behaviors include the ability to read…

We propose a novel system, MathMistake Checker, designed to automate step-by-step mistake finding in mathematical problems with lengthy answers through a two-stage process. The system aims to simplify grading, increase efficiency, and…

Assessing instruction quality is a fundamental component of any improvement efforts in the education system. However, traditional manual assessments are expensive, subjective, and heavily dependent on observers' expertise and idiosyncratic…

We introduce Goedel-Prover, an open-source language model that achieves state-of-the-art (as of April 5 2025) performance in automated formal proof generation for mathematical problems. A key challenge in this field is the scarcity of…

Fact verification systems typically rely on neural network classifiers for veracity prediction which lack explainability. This paper proposes ProoFVer, which uses a seq2seq model to generate natural logic-based inferences as proofs. These…

Interactive proof assistants are computer programs carefully constructed to check a human-designed proof of a mathematical claim with high confidence in the implementation. However, this only validates truth of a formal claim, which may…

Large pre-trained neural models have achieved remarkable success in natural language process (NLP), inspiring a growing body of research analyzing their ability from different aspects. In this paper, we propose a test suite to evaluate the…