相关论文: Theorie des groupes et psychologie de l'intelligen…

In this paper we define a new algebraic object: the disguised-groups. We show the main properties of the disguised-groups and, as a consequence, we will see that disguised-groups coincide with regular semigroups. We prove many of the…

In this paper we show that counting Grothendieck's dessins d'enfants is universal in the sense that some other enumerative problems are either special cases or directly related to it. Such results provide concrete examples that support a…

It is well known that the Galois group of an extension puts constraints on the structure of the relative ideal class groups. Using only basic parts of the theory of group representations, we give a unified approach to such results.

In these lecture notes, we give a quick account of the theory of Poisson groupoids and Lie bialgebroids. In particular, we discuss the universal lifting theorem and its applications including integration of quasi-Lie bialgebroids,…

Understanding realistic complex systems requires confronting significant conceptual, theoretical and experimental limitations rooted in the persistence of views that originated in the mechanics of simple moving bodies. We define the…

We use a novel type of epistemic logic, employing comparative knowledge assertions, to analyze the relative epistemic powers of individuals or groups of agents. Such comparative assertions can express that a group has the potential to…

Curiosity is a vital metacognitive skill in educational contexts, leading to creativity, and a love of learning. And while many school systems increasingly undercut curiosity by teaching to the test, teachers are increasingly interested in…

Wigner found unreasonable the "effectiveness of mathematics in the natural sciences". But if the mathematics we use to describe nature is simply a coded expression of our experience then its effectiveness is quite reasonable. Its…

These few pages briefly present the way in which Activity Theory has been adopted for several years now by French researchers in didactics of mathematics and has been adapted to study the learning of school mathematics in relation with the…

Understanding each other is the key to success in collaboration. For humans, attributing mental states to others, the theory of mind, provides the crucial advantage. We argue for formulating human--AI interaction as a multi-agent problem,…

The aim of this paper is to describe the definitions and main properties of three generalizations of the group concept, namely: groupoid, generalized group and almost groupoid. Some constructions of these algebraic structures and…

Game theory offers a powerful framework for analyzing strategic interactions among decision-makers, providing tools to model, analyze, and predict their behavior. However, implementing game theory can be challenging due to difficulties in…

We develop a generalised gauge theory in which the role of gauge group is played by a coalgebra and the role of principal bundle by an algebra. The theory provides a unifying point of view which includes quantum group gauge theory,…

In this paper, we will expound upon the concepts proffered in [1], where we proposed an information theoretic approach to intelligence in the computational sense. We will examine data and meme aggregation, and study the effect of limited…

Independent from the still ongoing research in measuring individual intelligence, we anticipate and provide a framework for measuring collective intelligence. Collective intelligence refers to the idea that several individuals can…

Toy models are highly idealized and deliberately simplified models that retain only the essential features of a system in order to explore specific theoretical questions. Long used in physics and other sciences, they have recently begun to…

We address the issue of the fallacy of the gauge concept in electromagnetism. The role of groupthink in the perpetuation of this concept in the physics literature is also discussed. Brief, elementary arguments suffice to demonstrate the…

Extensive work has been conducted both in game theory and logic to model strategic interaction. An important question is whether we can use these theories to design agents for interacting with people? On the one hand, they provide a formal…

Relying on recent generalizations of the Fra\"iss\'e theory to a broader category-theoretic context, we study the class of abstract finite games played between two players and show the existence of an infinitetly countable game which is…

An algebraic formalism for the study of interacting particle systems is developed. Particle processes are described in terms of the category theory. The problem for the unique description of these processes is discussed. Categories relevant…