Related papers: Teaching and learning mathematics with Prolog

The intention of these notes is to give a mathematical account of how I believe students could be taught to think about functional programming languages and to explain how such languages work.

This paper investigates the capabilities of large language models (LLMs) in formulating and solving decision-making problems using mathematical programming. We first conduct a systematic review and meta-analysis of recent literature to…

Code has become a standard component of modern foundation language model (LM) training, yet its role beyond programming remains unclear. We revisit the claim that code improves reasoning through controlled pretraining experiments on a…

Scientific computation is a discipline that combines numerical analysis, physical understanding, algorithm development, and structured programming. Several yottacycles per year on the world's largest computers are spent simulating problems…

Our position is that logic programming is not programming in the Horn clause sublogic of classical logic, but programming in a logic of (inductive) definitions. Thus, the similarity between prototypical Prolog programs (e.g., member,…

$\{log\}$ is a programming language at the intersection of Constraint Logic Programming, set programming and declarative programming. But $\{log\}$ is also a satisfiability solver for a theory of finite sets and finite binary relations.…

Aiming to offer a framework for blended learning to the teaching of proof theory, the present paper describes an interactive tutorial, called \textsc{TryLogic}, teaching how to solve logical conjectures either by proofs or refutations. The…

A simple mathematical definition of the 4-port model for pure Prolog is given. The model combines the intuition of ports with a compact representation of execution state. Forward and backward derivation steps are possible. The model…

Many interesting and useful symbolic computation algorithms manipulate mathematical expressions in mathematically meaningful ways. Although these algorithms are commonplace in computer algebra systems, they can be surprisingly difficult to…

In the former article "Formal mathematical systems including a structural induction principle" we have presented a unified theory for formal mathematical systems including recursive systems closely related to formal grammars, including the…

This paper presents a Prolog-based reasoning module to generate counterfactual explanations given the predictions computed by a black-box classifier. The proposed symbolic reasoning module can also resolve what-if queries using the…

Learning and logic are distinct and remarkable approaches to prediction. Machine learning has experienced a surge in popularity because it is robust to noise and achieves high performance; however, ML experiences many issues with knowledge…

The basic notions of logic-predicate logic, Peano arithmetic, incompleteness theorems, etc.-have for long been an advanced topic. In the last decades, they became more widely taught, inphilosophy, mathematics, and computer science…

A functional hardware description language enables students to gain a working understanding of computer systems, and to see how the levels of abstraction fit together. By simulating circuits, digital design becomes a living topic, like…

The search for information on the web is faced with several problems, which arise on the one hand from the vast number of available sources, and on the other hand from their heterogeneity. A promising approach is the use of multi-agent…

With the rapid rise of generative AI in higher education and the unreliability of current AI detection tools, developing policies that encourage student learning and critical thinking has become increasingly important. This study examines…

"Systems that Explain Themselves" appears a provocative wording, in particular in the context of mathematics education -- it is as provocative as the idea of building educational software upon technology from computer theorem proving. In…

A significant amount of research has considered mathematical proofs, the students who learn them, and the instructors that teach them, from a variety of perspectives. This paper considers this topic from four main perspectives: students'…

Checklists have been widely recognized as effective tools for completing complex tasks in a systematic manner. Although originally intended for use in procedural tasks, their interpretability and ease of use have led to their adoption for…

Logic reasoning has been critically needed in problem-solving and decision-making. Although Language Models (LMs) have demonstrated capabilities of handling multiple reasoning tasks (e.g., commonsense reasoning), their ability to reason…