Related papers: Prototyping "Systems that Explain Themselves" for …
Teaching college students how to write rigorous proofs is a critical objective in courses that introduce formal reasoning. Over the course of several years, we have developed a mechanically-checkable style of calculational reasoning that we…
Mathematical proofs are both paradigms of certainty and some of the most explicitly-justified arguments that we have in the cultural record. Their very explicitness, however, leads to a paradox, because the probability of error grows…
The CSCW community has a history of designing, implementing, and evaluating novel social interactions in technology, but the process requires significant technical effort for uncertain value. We discuss the opportunities and applications of…
Structural proof theory is praised for being a symbolic approach to reasoning and proofs, in which one can define schemas for reasoning steps and manipulate proofs as a mathematical structure. For this to be possible, proof systems must be…
Prototypical Learning is based on the idea that there is a point (which we call prototype) around which the embeddings of a class are clustered. It has shown promising results in scenarios with little labeled data or to design explainable…
In accordance with Bloom's taxonomy, a four-level evaluation abstraction was generated with the objective of structuring and hierarchizing curricula knowledge, allowing students to dominate a subject and progressively reach the top of…
Personalised education is one of the domains that can greatly benefit from the most recent advances in Artificial Intelligence (AI) and Large Language Models (LLM). However, it is also one of the most challenging applications due to the…
Formal methods yet advantageous, face challenges towards wide acceptance and adoption in software development practices. The major reason being presumed complexity. The issue can be addressed by academia with a thoughtful plan of teaching…
It is nowadays common to consider that proof must be part of the learning of mathematics from Kindergarten to University1. As it is easy to observe, looking back to the history of mathematical curricula, this has not always been the case…
This study explores the integration of generative artificial intelligence (AI), specifically large language models, with multi-modal analogical reasoning as an innovative approach to enhance science, technology, engineering, and mathematics…
Procedural computer languages have long been used in many aspects of mathematics pedagogy. In this work, we examine the use of Prolog, a declarative language for the same purpose. We find the facts+rules aspect of Prolog to be a novel…
Theorem proving is a fundamental aspect of mathematics, spanning from informal reasoning in natural language to rigorous derivations in formal systems. In recent years, the advancement of deep learning, especially the emergence of large…
In socio-technical settings, operators are increasingly assisted by decision support systems. By employing these, important properties of socio-technical systems such as self-adaptation and self-optimization are expected to improve further.…
The geometry automated theorem proving area distinguishes itself by a large number of specific methods and implementations, different approaches (synthetic, algebraic, semi-synthetic) and different goals and applications (from research in…
Modeling seeks to tame complexity during software development, by supporting design, analysis, and stakeholder communication. Paradoxically, experiences made by educators indicate that students often perceive modeling as adding complexity,…
Automated theorem provers and formal proof assistants are general reasoning systems that are in theory capable of proving arbitrarily hard theorems, thus solving arbitrary problems reducible to mathematics and logical reasoning. In…
Technology is currently ubiquitous and is also part of the educational system at all levels. It started with communication technology systems, and later continued with digital competence. Nowadays, although these previous concepts are still…
This paper develops an algorithmic-based approach for proving inductive properties of propositional sequent systems such as admissibility, invertibility, cut-elimination, and identity expansion. Although undecidable in general, these…
Recent work on interpretability in machine learning and AI has focused on the building of simplified models that approximate the true criteria used to make decisions. These models are a useful pedagogical device for teaching trained…
Circular (or cyclic) proofs have received increasing attention in recent years, and have been proposed as an alternative setting for studying (co)inductive reasoning. In particular, now several type systems based on circular reasoning have…