Related papers: Gentzen-Prawitz Natural Deduction as a Teaching To…
When demonstrating a task, human tutors pedagogically modify their behavior by either "showing" the task rather than just "doing" it (exaggerating on relevant parts of the demonstration) or by giving demonstrations that best disambiguate…
An interactive theorem prover, Isabelle, is under development. In LCF, each inference rule is represented by one function for forwards proof and another (a tactic) for backwards proof. In Isabelle, each inference rule is represented by a…
The black-box nature of neural models has motivated a line of research that aims to generate natural language rationales to explain why a model made certain predictions. Such rationale generation models, to date, have been trained on…
An on-line drilling system, the tutor-web, has been developed and used for teaching mathematics and statistics. The system was used in a basic course in calculus including 182 students. The students were requested to answer quiz questions…
LLM-as-a-Judge employs large language models (LLMs), such as GPT-4, to evaluate the quality of LLM-generated responses, gaining popularity for its cost-effectiveness and strong alignment with human evaluations. However, training proxy judge…
The aim of this study is to investigate the decisions and reasoning of undergraduate students when choosing simple measurement instruments in an introductory physics laboratory course. For this study, we have developed a questionnaire and…
After a large "teacher" neural network has been trained on labeled data, the probabilities that the teacher assigns to incorrect classes reveal a lot of information about the way in which the teacher generalizes. By training a small…
Lorenzen's ``Algebraische und logistische Untersuchungen \"uber freie Verb\"ande'' appeared in 1951 in The journal of symbolic logic. These ``Investigations'' have immediately been recognised as a landmark in the history of infinitary proof…
One of the goals of language model unlearning is to reduce memorization of selected text instances while retaining the model's general abilities. Despite various proposed methods, reducing memorization of large datasets without noticeable…
Formulating research questions is a foundational yet challenging academic skill, one that generative AI systems often oversimplify by offering instant answers at the expense of student reflection. This protocol lays out a study grounded in…
In recent years, many explanation methods have been proposed to explain individual classifications of deep neural networks. However, how to leverage the created explanations to improve the learning process has been less explored. As the…
Proof assistants are important tools for teaching logic. We support this claim by discussing three formalizations in Isabelle/HOL used in a recent course on automated reasoning. The first is a formalization of System W (a system of…
In functional programming, datatypes a la carte provide a convenient modular representation of recursive datatypes, based on their initial algebra semantics. Unfortunately it is highly challenging to implement this technique in proof…
One can notice that quite often difference between so-called "standard students" and "gifted" ones is not because that first are less smart, but they have different "orientation", they consider subject as a collections of rules which should…
Natural philosophy integrates scientific observation with abstract frameworks, often using a mathematical Ansatz to hypothesise about physical phenomena. Exploring the possibility of other universes, however, challenges assumptions that…
Undergraduate students of artificial intelligence often struggle with representing knowledge as logical sentences. This is a skill that seems to require extensive practice to obtain, suggesting a teaching strategy that involves the…
Explicit density learners are becoming an increasingly popular technique for generative models because of their ability to better model probability distributions. They have advantages over Generative Adversarial Networks due to their…
This paper presents a formal theory which describes propositional binary logic as a semantically closed formal language, and allows for syntactically and semantically well-formed formulae, formal proofs (demonstrability in Hilbertian…
Explanation constitutes an archetypal feature of human rationality, underpinning learning and generalisation, and representing one of the media supporting scientific discovery and communication. Due to the importance of explanations in…
Intelligent tutoring systems have long enabled automated immediate feedback on student work when it is presented in a tightly structured format and when problems are very constrained, but reliably assessing free-form mathematical reasoning…