Related papers: Natural Language Proof Checking in Introduction to…
Chain-of-Thought reasoning has emerged as a powerful approach for solving complex mathematical and logical problems. However, it can often veer off track through incorrect or unsubstantiated inferences. Formal mathematical reasoning, which…
Demonstration learning aims to guide the prompt prediction via providing answered demonstrations in the few shot settings. Despite achieving promising results, existing work only concatenates the answered examples as demonstrations to the…
Background: Proof Blocks is a software tool that enables students to construct proofs by assembling prewritten lines and gives them automated feedback. Prior work on learning gains from Proof Blocks has focused on comparing learning gains…
Proof scores can be regarded as outlines of the formal verification of system properties. They have been historically used by the OBJ family of specification languages. The main advantage of proof scores is that they follow the same syntax…
We introduce a task consisting in matching a proof to a given mathematical statement. The task fits well within current research on Mathematical Information Retrieval and, more generally, mathematical article analysis (Mathematical…
Numerical reasoning over natural language has been a long-standing goal for the research community. However, cutting-edge language models have proven difficult to reliably generalize to a broad range of numbers, although they have shown…
In France, the first year of study at university is usually abbreviated L1 (for premiere annee de Licence). At Sorbonne Paris Nord University, we have been teaching an 18 hour introductory course in formal proofs to L1 students for 3 years.…
Introductory programming courses often rely on small code-writing exercises that have clearly specified problem statements. This limits opportunities for students to practice how to clarify ambiguous requirements -- a critical skill in…
We introduce ProofNet, a benchmark for autoformalization and formal proving of undergraduate-level mathematics. The ProofNet benchmarks consists of 371 examples, each consisting of a formal theorem statement in Lean 3, a natural language…
We design a proof system for propositional classical logic that integrates two languages for Boolean functions: standard conjunction-disjunction-negation and binary decision trees. We give two reasons to do so. The first is…
The sequent calculus is a formalism for proving validity of statements formulated in First-Order Logic. It is routinely used in computer science modules on mathematical logic. Formal proofs in the sequent calculus are finite trees obtained…
Feedback is a critical aspect of improvement. Unfortunately, when there is a lot of feedback from multiple sources, it can be difficult to distill the information into actionable insights. Consider student evaluations of teaching (SETs),…
We report a four-years experiment in teaching reasoning to undergraduate students, ranging from weak to gifted, using Gentzen-Prawitz's style natural deduction. We argue that this pedagogical approach is a good alternative to the use of…
Grammar checking is the task of detection and correction of grammatical errors in the text. English is the dominating language in the field of science and technology. Therefore, the non-native English speakers must be able to use correct…
On-the-job learning consists in continuously learning while being used in production, in an open environment, meaning that the system has to deal on its own with situations and elements never seen before. The kind of systems that seem to be…
These are the notes for a 5-lecture-course given at ESSLLI 2006 in Malaga, Spain. The URL of the school is http://esslli2006.lcc.uma.es/ . This version slightly differs from the one which has been distributed at the school because typos…
Question Answering has recently received high attention from artificial intelligence communities due to the advancements in learning technologies. Early question answering models used rule-based approaches and moved to the statistical…
The combination of verifiable languages and LLMs has significantly influenced both the mathematical and computer science communities because it provides a rigorous foundation for theorem proving. Recent advancements in the field provide…
The detection of disfluencies such as hesitations, repetitions and false starts commonly found in speech is a widely studied area of research. With a standardised process for evaluation using the Switchboard Corpus, model performance can be…
In formal proof checking environments such as Mizar it is not merely the validity of mathematical formulas that is evaluated in the process of adoption to the body of accepted formalizations, but also the readability of the proofs that…