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This work examines the interconnections between logic, epistemology, and sciences within the Naturalist tradition. It presents a scheme that connects logic, mathematics, physics, chemistry, biology, and cognition, emphasizing…
This document presents endeavors to represent emotion in a computational cognitive architecture. The first part introduces research organizing with two axes of emotional affect: pleasantness and arousal. Following this basic of emotional…
We propose a simple cognitive model where qualitative and quantitative com- parisons enable animals to identify objects, associate them with their properties held in memory and make naive inference. Simple notions like equivalence re-…
We give an overview of our philosophy of pictures in mathematics. We emphasize a bi-directional process between picture language and mathematical concepts: abstraction and simulation. This motivates a program to understand different…
There are many scientific problems generated by the multiple and conflicting alternative definitions of linguistic recursion and human recursive processing that exist in the literature. The purpose of this article is to make available to…
Math is constructed by people for people: just as natural language corpora reflect not just propositions but the communicative goals of language users, the math data that models are trained on reflects not just idealized mathematical…
Mathematical maturity is a key concept for the professional life of a mathematician. This paper is not only a brief discussion of the importance of mathematical maturity but also presents some unusual ways we can use the concept to help our…
Most approaches to emotion analysis of social media, literature, news, and other domains focus exclusively on basic emotion categories as defined by Ekman or Plutchik. However, art (such as literature) enables engagement in a broader range…
This essay examines the relationship between artificial intelligence and the historical evolution of modern Mathematics. Rather than viewing AI as an external rupture, we argue that its effectiveness reveals a structural tendency already…
In this paper we use theoretical frameworks from mathematics education and cognitive psychology to analyse Cauchy's ideas of function, continuity, limit and infinitesimal expressed in his Cours D'Analyse. Our analysis focuses on the…
A new generation of educational mathematics software is being shaped in ThEdu and other academic communities on the side of computer mathematics. Respective concepts and technologies have been clarified to an extent, which calls for…
In the paper, the authors elaborate some recently published research concerning the originality of artworks in terms of self-organization in the complex systems physics. It has been demonstrated that the originality issue such conceived…
Mathematical understanding is built in many ways. Among these, illustration has been a companion and tool for research for as long as research has taken place. We use the term illustration to encompass any way one might bring a mathematical…
In this paper we examine the concept of complexity as it applies to generative and evolutionary art and design. Complexity has many different, discipline specific definitions, such as complexity in physical systems (entropy), algorithmic…
Many prominent lines of research on student's reasoning and conceptual change within learning sciences and physics education research have not attended to the role of learners' affect or emotions in the dynamics of their conceptual…
We present a general logical framework for reasoning about agents' cognitive attitudes of both epistemic type and motivational type. We show that it allows us to express a variety of relevant concepts for qualitative decision theory…
Affective computing has proven to be a viable field of research comprised of a large number of multidisciplinary researchers resulting in work that is widely published. The majority of this work consists of computational models of emotion…
Cognitive modeling, which explores the essence of cognition, including motivation, emotion, and perception, has been widely applied in the artificial intelligence (AI) agent domains, such as robotics. From the computational perspective,…
The fundamental role of mathematics as an inspiration for artists, but also as a tool for art creation, is presented in this paper following different art fields, like architecture, sculpture, painting, photography, literature and poetry,…
Computational imaging has been playing a vital role in the development of natural sciences. Advances in sensory, information, and computer technologies have further extended the scope of influence of imaging, making digital images an…