Related papers: Formal Ways for Measuring Relations between Concep…
In this paper we will present an ongoing project which aims to use model theory as a suitable mathematical setting for studying the formalism of quantum mechanics. We will argue that this approach provides a geometric semantics for such…
In this introductory article we present the basics of an approach to implementing computational interpreting of natural language aiming to model the meanings of words and phrases. Unlike other approaches, we attempt to define the meanings…
The mathematical formalism of quantum theory exhibits significant effectiveness when applied to cognitive phenomena that have resisted traditional (set theoretical) modeling. Relying on a decade of research on the operational foundations of…
Regions-based theories of space aim -- among others -- to define points in a geometrically appealing way. The most famous definition of this kind is probably due to Whitehead. However, to conclude that the objects defined are points indeed,…
This article is an exploratory account of the the non-monotonic behaviour of conceptual associations in the light of context. Computational approximations of conceptual space are furnished by semantic space models which are emerging from…
Shape information is crucial for human perception and cognition, and should therefore also play a role in cognitive AI systems. We employ the interdisciplinary framework of conceptual spaces, which proposes a geometric representation of…
When considering perceptions, the observation scale and resolution are closely related properties. There is consensus in considering resolution as the density of elementary pieces of information in a specified information space.…
In this chapter tools and techniques from the mathematical theory of formal concept analysis are applied to hypertext systems in general, and the World Wide Web in particular. Various processes for the conceptual structuring of hypertext…
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…
The visual representation of concepts or ideas through the use of simple shapes has always been explored in the history of Humanity, and it is believed to be the origin of writing. We focus on computational generation of visual symbols to…
Quantifying the degree of similarity between images is a key copyright issue for image-based machine learning. In legal doctrine however, determining the degree of similarity between works requires subjective analysis, and fact-finders…
Researchers have derived many theoretical models for specifying users' insights as they interact with a visualization system. These representations are essential for understanding the insight discovery process, such as when inferring user…
This paper explores the hard problem of consciousness from a different perspective. Instead of drawing distinctions between the physical and the mental, an exploration of a more foundational relationship is examined: the relationship…
Measurements play a crucial role in doing physics: Their results provide the basis on which we adopt or reject physical theories. In this note, we examine the effect of subjecting measurements themselves to our experience. We require that…
This work introduces a framework for quantifying the information content of logical propositions through the use of implication hypergraphs. We posit that a proposition's informativeness is primarily determined by its relationships with…
Conceptual entanglement is a crucial phenomenon in quantum cognition because it implies that classical probabilities cannot model non--compositional conceptual phenomena. While several psychological experiments have been developed to test…
High-dimensional representations for words, text, images, knowledge graphs and other structured data are commonly used in different paradigms of machine learning and data mining. These representations have different degrees of…
Neural network models of language have long been used as a tool for developing hypotheses about conceptual representation in the mind and brain. For many years, such use involved extracting vector-space representations of words and using…
We extend a newly developed formal system for the description of astrophysical maps. In this formalism, we consider the difference between maps to be the distance between elements of a pseudometric space (the space of all such maps). This…
This is a write-up of a talk given at the CATMI meeting in Bergen in July 2023, and is an introduction to a category-theoretic perspective on metric spaces. A metric space is a set of points such that between each pair of points there is a…