Related papers: A Comprehensive Implementation of Conceptual Space…
Here we will discuss the philosophical differences between an approach to the deep nature of physical space based on the concept of coordinates and one based on the concept of relation. The philosophical superiority of the second approach…
While the interpretation of high-dimensional datasets has become a necessity in most industries, and is supported by continuous advances in data science and machine learning, the spatial visualization of higher-dimensional geometry has…
Human knowledge provides a formal understanding of the world. Knowledge graphs that represent structural relations between entities have become an increasingly popular research direction towards cognition and human-level intelligence. In…
Taxonomies are semantic hierarchies of concepts. One limitation of current taxonomy learning systems is that they define concepts as single words. This position paper argues that contextualized word representations, which recently achieved…
Despite ample evidence that our concepts, our cognitive architecture, and mathematics itself are all deeply compositional, few models take advantage of this structure. We therefore propose a radically compositional approach to computational…
The ability to persist in the spacial environment is, not only in the robotic context, an essential feature. Positional knowledge is one of the most important aspects of space and a number of methods to represent these information have been…
I present a framework based on the concepts of diversity and coherence for the analysis of knowledge integration and diffusion. Visualisations that help understand insights gained are also introduced. The key novelty offered by this…
Represented spaces form the general setting for the study of computability derived from Turing machines. As such, they are the basic entities for endeavors such as computable analysis or computable measure theory. The theory of represented…
Learning Spaces are certain set systems that are applied in the mathematical modeling of education. We propose a suitable compression (without loss of information) of such set systems to facilitate their logical and statistical analysis.…
Conceptual spaces represent entities and concepts using cognitively meaningful dimensions, typically referring to perceptual features. Such representations are widely used in cognitive science and have the potential to serve as a…
While many methods for learning vector space embeddings have been proposed in the field of Natural Language Processing, these methods typically do not distinguish between categories and individuals. Intuitively, if individuals are…
Humans are able to conceive physical reality by jointly learning different facets thereof. To every pair of notions related to a perceived reality may correspond a mutual relation, which is a notion on its own, but one-level higher. Thus,…
Using ideas from synthetic topology, a new approach to descriptive set theory is suggested. Synthetic descriptive set theory promises elegant explanations for various phenomena in both classic and effective descriptive set theory.…
Conceptualization, a fundamental element of human cognition, plays a pivotal role in human generalizable reasoning. Generally speaking, it refers to the process of sequentially abstracting specific instances into higher-level concepts and…
Despite the centrality of the notion of representation in neuroscience, the field lacks a unified framework for the concepts used to characterize representation, leading to disparate use of both terminology and measures associated with it.…
The concept of synthetic dimensions has emerged as a powerful framework in photonics and atomic physics, enabling the exploration of high-dimensional physics beyond conventional spatial constraints. Originally developed for quantum…
The Artificial Intelligence field is flooded with optimisation methods. In this paper, we change the focus to developing modelling methods with the aim of getting us closer to Artificial General Intelligence. To do so, we propose a novel…
This paper attempts to synthesize various conceptualizations of the term "context" as found in computing literature. Ten conceptual dimensions of context thus emerge -- location; user, task, and system characteristics; physical, social,…
This article presents a concept-centric paradigm for building agents that can learn continually and reason flexibly. The concept-centric agent utilizes a vocabulary of neuro-symbolic concepts. These concepts, such as object, relation, and…
Formal definitions of quantities, quantity spaces, dimensions and dimension groups are introduced. Based on these concepts, a theoretical framework and a practical algorithm for dimensional analysis are developed, and examples of…