Related papers: A Thorough Formalization of Conceptual Spaces
Traditional neural embeddings represent concepts as points, excelling at similarity but struggling with higher-level reasoning and asymmetric relationships. We introduce a novel paradigm: embedding concepts as linear subspaces. This…
Human cognition is a complex process facilitated by the intricate architecture of human brain. However, human cognition is often reduced to quantum theory based events in principle because of their correlative conjectures for the purpose of…
This paper further studies the fuzzy rough sets based on fuzzy coverings. We first present the notions of the lower and upper approximation operators based on fuzzy coverings and derive their basic properties. To facilitate the computation…
Emergences of computers and information technological revolution made tremendous changes in the real world and provides a different dimension for the intelligent data analysis. Well formed fact, the information at right time and at right…
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.…
This article deals with the description and recognition of fiber bundles, in particular nerves, in medical images, based on the anatomical description of the fiber trajectories. To this end, we propose a logical formalization of this…
Concept discovery is one of the open problems in the interpretability literature that is important for bridging the gap between non-deep learning experts and model end-users. Among current formulations, concepts defines them by as a…
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,…
The cognitive framework of conceptual spaces [3] provides geometric means for representing knowledge. A conceptual space is a high-dimensional space whose dimensions are partitioned into so-called domains. Within each domain, the Euclidean…
The definition of the complement of a fuzzy subset is algebraic in nature and when it is used in the context of fuzzy topological spaces it does not share any similarity with the usual property of topological spaces that the complement of…
Formal concept analysis has grown from a new branch of the mathematical field of lattice theory to a widely recognized tool in Computer Science and elsewhere. In order to fully benefit from this theory, we believe that it can be enriched…
We present modeling for conceptual combinations which uses the mathematical formalism of quantum theory. Our model faithfully describes a large amount of experimental data collected by different scholars on concept conjunctions and…
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…
Learning structured representations of visual scenes is currently a major bottleneck to bridging perception with reasoning. While there has been exciting progress with slot-based models, which learn to segment scenes into sets of objects,…
Taxonomy Expansion, which models complex concepts and their relations, can be formulated as a set representation learning task. The generalization of set, fuzzy set, incorporates uncertainty and measures the information within a semantic…
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…
Hyperspaces form a powerful tool in some branches of mathematics: lots of fractal and other geometric objects can be viewed as fixed points of some functions in suitable hyperspaces - as well as interesting classes of formal languages in…
We revisit the design space of visualizations aiming at identifying and relating its components. In this sense, we establish a model to examine the process through which visualizations become expressive for users. This model has leaded us…
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…
We define a symmetric monoidal category modelling fuzzy concepts and fuzzy conceptual reasoning within G\"ardenfors' framework of conceptual (convex) spaces. We propose log-concave functions as models of fuzzy concepts, showing that these…