Related papers: Logic Modelling
I have developed a pedagogy and textbook for teaching logic centered on what I call "logical worldviews". A logical worldview examines the close connection between philosophical commitments and the logical principles and method for a…
Logical reasoning is essential in a variety of human activities. A representative example of a logical task is mathematics. Recent large-scale models trained on large datasets have been successful in various fields, but their reasoning…
We introduce a logic for reasoning about evidence that essentially views evidence as a function from prior beliefs (before making an observation) to posterior beliefs (after making the observation). We provide a sound and complete…
Given the importance of integrating of explainability into machine learning, at present, there are a lack of pedagogical resources exploring this. Specifically, we have found a need for resources in explaining how one can teach the…
A primary goal of physics is to create mathematical models that allow both predictions and explanations of physical phenomena. We weave maths extensively into our physics instruction beginning in high school, and the level and complexity of…
Studying Mathematics requires a synthesis of skills from a multitude of academic disciplines; logical reasoning being chief among them. This paper explores mathematical logical preparedness of students entering first year university…
We report on several scenarios of using automated theorem proving software in university education. In particular, we focus on using the Theorema system in a software-enhanced logic-course for students in computer science or artificial…
The design of any technical Computer Science course must involve its context within the institution's CS program, but also incorporate any new material that is relevant and appropriately accessible to students. In many institutions, theory…
Large Language Models (LLMs) have demonstrated impressive capabilities in structured reasoning and symbolic tasks, with coding emerging as a particularly successful application. This progress has naturally motivated efforts to extend these…
My purpose is to examine some concepts of mathematical logic, which have been studied by Carlo Cellucci. Today the aim of classical mathematical logic is not to guarantee the certainty of mathematics, but I will argue that logic can help us…
Mastering one or more programming languages has historically been the gateway to implementing ideas on a computer. Today, that gateway is widening with advances in large language models (LLMs) and artificial intelligence (AI)-powered coding…
An origin is often an intriguing issue. It becomes doubly intriguing when the logical form of thinking is considered. In this paper we will investigate exactly that: we will conjecture on the origin of basic instruments of logical thinking.…
Basic principles of mathematical modeling are reviewed in this book, with the focus on physics and its practical applications, and examples of selected mathematical methods are presented. Most of the models have been imported from physics…
This paper argues that large language models have a valuable scientific role to play in serving as scientific models of public languages. Linguistic study should not only be concerned with the cognitive processes behind linguistic…
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,…
First-order logic is typically presented as the study of deduction in a setting with elementary quantification. In this paper, we take another vantage point and conceptualize first-order logic as a linear space that encodes "plausibility".…
Logic has its origins in basic questions about the nature of the real world and how we describe it. This article seeks to bring out the physical and epistemological relevance of some of the more recent technical work in logic and…
The importance of transformations and normal forms in logic programming, and generally in computer science, is well documented. This paper investigates transformations and normal forms in the context of Defeasible Logic, a simple but…
Mathematical modelling and ethics have more touching points than most of us would like to admit. Everyday decisions are often reasoned by mathematical arguments. Mathematics teachers belong to those mathematically literate, who must point…
Modeling the logical architecture is an often underestimated development step to gain an early insight into the fundamental functional properties of an automotive system. An architectural description supports developers in making design…