Graph Representations for Higher-Order Logic and Theorem Proving

This paper presents the first use of graph neural networks (GNNs) for higher-order proof search and demonstrates that GNNs can improve upon state-of-the-art results in this domain. Interactive, higher-order theorem provers allow for the formalization of most mathematical theories and have been shown to pose a significant challenge for deep learning. Higher-order logic is highly expressive and, even though it is well-structured with a clearly defined grammar and semantics, there still remains no well-established method to convert formulas into graph-based representations. In this paper, we consider several graphical representations of higher-order logic and evaluate them against the HOList benchmark for higher-order theorem proving

Building communities for the exchange of learning objects: theoretical foundations and requirements

In order to reduce overall costs of developing high-quality digital courses (including both the content, and the learning and teaching activities), the exchange of learning objects has been recognized as a promising solution. This article makes an inventory of the issues involved in the exchange of learning objects within a community. It explores some basic theories, models and specifications and provides a theoretical framework containing the functional and non-functional requirements to establish an exchange system in the educational field. Three levels of requirements are discussed. First, the non-functional requirements that deal with the technical conditions to make learning objects interoperable. Second, some basic use cases (activities) are identified that must be facilitated to enable the technical exchange of learning objects, e.g. searching and adapting the objects. Third, some basic use cases are identified that are required to establish the exchange of learning objects in a community, e.g. policy management, information and training. The implications of this framework are then discussed, including recommendations concerning the identification of reward systems, role changes and evaluation instruments

Theories of the evolution of cooperative behaviour: A critical survey plus some new results

Gratuitous cooperation (in favour of non-relatives and without repeated interaction) eludes traditional evolutionary explanations. In this paper we survey the various theories of cooperative behaviour, and we describe our own effort to integrate these theories into a self-contained framework. Our main conclusions are as follows. First: altruistic punishment, conformism and gratuitous cooperation co-evolve, and group selection is a necessary ingredient for the co-evolution to take place. Second: people do not cooperate by mistake, as most theories imply; on the contrary, people knowingly sacrifice themselves for others. Third: in cooperative dilemmas conformism is an expression of preference, not a learning rule. Fourth, group-mutations (e.g., the rare emergence of a charismatic leader that brings order to the group) are necessary to sustain cooperation in the long run.Cooperation; altruism; altruistic punishment; conformism; group-selection

Theoretical and Conceptual Approaches to Co-Regulation: A Theoretical Review

During the last two decades, interpersonal regulation in natural and digital learning environments has gained importance. Ever since the first conceptual and methodological precisions regarding collaborative learning were made, educational psychology has focused its interest on analyzing collective regulation of motivation, cognition, and behavior. Despite the fact that the body of research on co-regulation has grown, emerging epistemological frameworks evidence a lack of conceptual and theoretical clarity. In response to this situation, the authors propose a conceptual approach in order to address interpersonal regulation in four aspects: first, they describe three learning theories which have been used to study co-regulation. Second, the authors recommend a conceptual delimitation of terms regarding the learning theories on social regulation. Third, they highlight diffuse boundaries between theoretical approaches and terms used in the literature on co-regulation. Finally, the authors suggest some challenges the researchers in this field face

The Concept and Context of Distance Learning in the New Normal Learning Scheme

Distance Learning has been around since its advent in 1960 and evolved in the creation of World Wide Web (WWW) in 1991 with the introduction of first education programs through internet of University of Phoenix and other universities and colleges. Vast ideas of concepts, theories and context have aroused in the popularization and implementation of distance learning in educational system and its first and most adversary are those in favor of lecture style of teaching. In the onset of the COVID-19, all fields of society have been affected and one of it is the educational system. This pandemic propagated the rise of distance learning in the Philippines and it becomes the most reliable modality of continuing the academic years. Distance learning becomes more adaptive and effective with the help of flexible teaching and learning modalities. Several studies exposed the concepts and theories for the distance learning to be more acceptable. These concepts and theories are supported by the literature with claims of context of distance learning in order to create an open and good system. Frameworks and being literate with the aid of continuous studies in this rising field is one of the key concepts in creating more possibilities to attain the quality of sufficient distance learning modality