Related papers: Gentzen-Prawitz Natural Deduction as a Teaching To…
A detailed exposition of foundations of a logic-algebraic model for reasoning with knowledge bases specified by propositional (Boolean) logic is presented. The model is conceived from the logical translation of usual derivatives on…
This paper explores the connection between two central results in the proof theory of classical logic: Gentzen's cut-elimination for the sequent calculus and Herbrands "fundamental theorem". Starting from Miller's expansion-tree-proofs, a…
Developing expert-like problem-solving skills is a central goal of undergraduate physics education. In this study, we investigate the impact of teaching explicit problem-solving frameworks, combined with deliberate practice, on students'…
This paper describes how automated deduction methods for natural language processing can be applied more efficiently by encoding context in a more elaborate way. Our work is based on formal approaches to context, and we provide a tableau…
Developing a suggestion by Russell, Prawitz showed how the usual natural deduction inference rules for disjunction, conjunction and absurdity can be derived using those for implication and the second order quantifier in propositional…
Inference systems are a widespread framework used to define possibly recursive predicates by means of inference rules. They allow both inductive and coinductive interpretations that are fairly well-studied. In this paper, we consider a…
This study aims to observe if the theorem prover Lean positively influences students' understanding of mathematical proving. To this end, we perform a pilot study concerning freshmen students at the University of Zurich (UZH). While doing…
We introduce judgemental theories and their calculi as a general framework to present and study deductive systems. As an exemplification of their expressivity, we approach dependent type theory and natural deduction as special kinds of…
Many mathematicians find mathematics aesthetically beautiful and even comparable to art forms such as music or painting. On the other hand, every year a great number of school students leave mathematics with total disillusionment and…
This chapter provides a hands-on tutorial on the important technique known as self-reducibility. Through a series of "Challenge Problems" that are theorems that the reader will---after being given definitions and tools---try to prove, the…
The technological and digital reality has broadly expanded, reaching the school. Therefore, this research aims to develop a didactic sequence, using as strategy a comic book, Figures, Gifs and videos, programs for activities applied to…
Demonstration is an appealing way for humans to provide assistance to reinforcement-learning agents. Most approaches in this area view demonstrations primarily as sources of behavioral bias. But in sparse-reward tasks, humans seem to treat…
Large natural language models (such as GPT-3 or T5) demonstrate impressive abilities across a range of general NLP tasks. Here, we show that the knowledge embedded in such models provides a useful inductive bias, not just on traditional NLP…
The learning process is a process of communication and interaction between the teacher and his students on one side and between the students and each others on the other side. Interaction of the teacher with his students has a great…
Almost from the inception of Hilbert's program, foundational and structural efforts in proof theory have been directed towards the goal of clarifying the computational content of modern mathematical methods. This essay surveys various…
Drawing inference from data is an important skill for students to understand their everyday life, so that the sampling distribution as a central topic in statistical inference is necessary to be learned by the students. However, little is…
Teachers intentionally pick the most informative examples to show their students. However, if the teacher and student are neural networks, the examples that the teacher network learns to give, although effective at teaching the student, are…
Recent empirical work has shown that human children are adept at learning and reasoning with probabilities. Here, we model a recent experiment investigating the development of school-age children's non-symbolic probability reasoning ability…
This is a companion to a paper by the authors entitled "G\"odel's natural deduction", which presented and made comments about the natural deduction system in G\"odel's unpublished notes for the elementary logic course he gave at the…
Physics education researchers are interested in using the tools of machine learning and natural language processing to make quantitative claims from natural language and text data, such as open-ended responses to survey questions. The…