Related papers: A Comprehensive Implementation of Conceptual Space…
Modelling concept representation is a foundational problem in the study of cognition and linguistics. This work builds on the confluence of conceptual tools from G\"ardenfors semantic spaces, categorical compositional linguistics, and…
This paper introduces the concept of spatial conceptual modeling, which allows anchoring mental world knowledge in the physical world using augmented reality technologies. For a first formal characterization, we describe a mapping from the…
Using the previously developed concepts of semantic spacetime, I explore the interpretation of knowledge representations, and their structure, as a semantic system, within the framework of promise theory. By assigning interpretations to…
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,…
We propose applying the categorical compositional scheme of [6] to conceptual space models of cognition. In order to do this we introduce the category of convex relations as a new setting for categorical compositional semantics, emphasizing…
We present the first steps of interaction spaces theory, a universal mathematical theory of complex systems which is able to embed cellular automata, agent based models, master equation based models, stochastic or deterministic, continuous…
The notion of a coherent space is a nonlinear version of the notion of a complex Euclidean space: The vector space axioms are dropped while the notion of inner product is kept. Coherent spaces provide a setting for the study of geometry in…
During the last decades, many cognitive architectures (CAs) have been realized adopting different assumptions about the organization and the representation of their knowledge level. Some of them (e.g. SOAR [Laird (2012)]) adopt a classical…
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…
In order to interact with objects in our environment, humans rely on an understanding of the actions that can be performed on them, as well as their properties. When considering concrete motor actions, this knowledge has been called the…
In this chapter, we assume that systematically studying spatial markers semantics in language provides a means to reveal fundamental properties and concepts characterizing conceptual representations of space. We propose a formal system…
We present a conceptual space framework for modelling abstract concepts that unfold over time, demonstrated through a chess-based proof-of-concept. Strategy concepts, such as attack or sacrifice, are represented as geometric regions across…
High-dimensional distributed semantic spaces have proven useful and effective for aggregating and processing visual, auditory, and lexical information for many tasks related to human-generated data. Human language makes use of a large and…
Representing the semantics of linguistic items in a machine-interpretable form has been a major goal of Natural Language Processing since its earliest days. Among the range of different linguistic items, words have attracted the most…
Inferential relations govern our concept use. In order to understand a concept it has to be located in a space of implications. There are different kinds of conditions for statements, i.e. that the conditions represent different kinds of…
In this paper, we present a constructive generalization of metric and uniform spaces by introducing a new class of spaces, called cover spaces. These spaces form a topological concrete category with a full reflective subcategory of complete…
We present a computational model for the semantic interpretation of symmetry in naturalistic scenes. Key features include a human-centred representation, and a declarative, explainable interpretation model supporting deep semantic…
In the paper a new programming construct, called concept, is introduced. Concept is pair of two classes: a reference class and an object class. Instances of the reference classes are passed-by-value and are intended to represent objects.…
This paper presents a geometric approach to the problem of modelling the relationship between words and concepts, focusing in particular on analogical phenomena in language and cognition. Grounded in recent theories regarding geometric…
Visualization researchers and visualization professionals seek appropriate abstractions of visualization requirements that permit considering visualization solutions independently from specific problems. Abstractions can help us design,…