Related papers: Prototyping "Systems that Explain Themselves" for …
Artificial intelligence now outperforms humans in several scientific and engineering tasks, yet its internal representations often remain opaque. In this Perspective, we argue that explainable artificial intelligence (XAI), combined with…
Models of physical systems are used to explain and predict experimental results and observations. The Modeling Framework for Experimental Physics describes the process by which physicists revise their models to account for the newly…
Large Language Models (LLMs) have demonstrated significant promise in formal theorem proving. In this study, we investigate the ability of LLMs to discover novel theorems and produce verified proofs. We propose a pipeline called…
The rapid adoption of generative artificial intelligence (AI) in educational assessment has created new opportunities for scalable item creation, personalized feedback, and efficient formative evaluation. However, despite advances in…
This paper describes a procedure that system developers can follow to translate typical mathematical representations of linearized control systems into logic theories. These theories are then used to verify system requirements and find…
Computational Logic is the use of computers to establish facts in a logical formalism. Originating in 19th-century attempts to understand the nature of mathematical reasoning, the subject now comprises a wide variety of formalisms,…
The prop formalism allows representation of processes withstring diagrams and has been successfully applied in various areas such as quantum computing, electric circuits and control flow graphs. However, these graphical approaches suffer…
Mathematical theorems are human knowledge able to be accumulated in the form of symbolic representation, and proving theorems has been considered intelligent behavior. Based on the BHK interpretation and the Curry-Howard isomorphism, proof…
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…
This paper summarizes our experience in communicating the elements of reasoning about correctness, and the central role of formal specifications in reasoning about modular, component-based software using a language and an integrated Web IDE…
Contribution: This study examined student effort and performance in an introductory programming course with respect to student-held implicit theories and self-efficacy. Background: Implicit theories and self-efficacy shed a light into…
The shortage of people trained in STEM fields is becoming acute, and universities and colleges are straining to satisfy this demand. In the case of computer science, for instance, the number of US students taking introductory courses has…
This paper presents a plausible reasoning system to illustrate some broad issues in knowledge representation: dualities between different reasoning forms, the difficulty of unifying complementary reasoning styles, and the approximate nature…
This panel draws on research of the teaching of mathematical proof, conducted in five countries at different levels of schooling. With a shared view of proof as essential to the teaching and learning of mathematics, the authors present…
The paper examines the construction of a course in mathematical analysis at a pedagogical university, aimed at developing the ability of future mathematics teachers to detect and solve problems related to finding proofs. Key words: teaching…
This chapter is interested in the epistemology of algorithms. As I intend to approach the topic, this is an issue about epistemic justification. Current approaches to justification emphasize the transparency of algorithms, which entails…
Contribution: In this study, an alternative educational approach for introducing quantum computing to a wider audience is highlighted. The proposed methodology considers quantum computing as a generalized probability theory rather than a…
Computational science and engineering (CSE) has been misunderstood to advance with the construction of enormous computers. To the contrary, the historical record demonstrates that innovations in CSE come from improvements to the mathematics…
Cognitive computing (COC) aims to embed human cognition into computerized models. However, there is no scientific classification that delineates the nature of Cognitive Computing. Unlike the medical and computer science fields, Information…
This is a survey on propositional proof complexity aimed at introducing the basics of the field with a particular focus on a method known as feasible interpolation. This method is used to construct "hard theorems" for several proof systems…