On Representing Concepts in High-dimensional Linear Spaces

Producing a mathematical model of concepts is a very important issue in artificial intelligence, because if such a model were found this, besides being a very interesting result in its own right, would also contribute to the emergence of what we could call the \u2018mathematics of thought.\u2019 One of the most interesting attempts made in this direction is P. Gardenfors\u2019 theory of conceptual spaces, a \ua8 theory which is mostly presented by its author in an informal way. The main aim of the present article is contributing to Gardenfors\u2019 theory of conceptual spaces \ua8 by discussing some of the advantages which derive from the possibility of representing concepts in high-dimensional linear spaces

Measuring Relations Between Concepts In Conceptual Spaces

The highly influential framework of conceptual spaces provides a geometric way of representing knowledge. Instances are represented by points in a high-dimensional space and concepts are represented by regions in this space. Our recent mathematical formalization of this framework is capable of representing correlations between different domains in a geometric way. In this paper, we extend our formalization by providing quantitative mathematical definitions for the notions of concept size, subsethood, implication, similarity, and betweenness. This considerably increases the representational power of our formalization by introducing measurable ways of describing relations between concepts.Comment: Accepted at SGAI 2017 (http://www.bcs-sgai.org/ai2017/). The final publication is available at Springer via https://doi.org/10.1007/978-3-319-71078-5_7. arXiv admin note: substantial text overlap with arXiv:1707.05165, arXiv:1706.0636

Platonic model of mind as an approximation to neurodynamics

Hierarchy of approximations involved in simplification of microscopic theories, from sub-cellural to the whole brain level, is presented. A new approximation to neural dynamics is described, leading to a Platonic-like model of mind based on psychological spaces. Objects and events in these spaces correspond to quasi-stable states of brain dynamics and may be interpreted from psychological point of view. Platonic model bridges the gap between neurosciences and psychological sciences. Static and dynamic versions of this model are outlined and Feature Space Mapping, a neurofuzzy realization of the static version of Platonic model, described. Categorization experiments with human subjects are analyzed from the neurodynamical and Platonic model points of view