Related papers: A Thorough Formalization of Conceptual Spaces

We present an approach for representing abstract argumentation frameworks based on an encoding into classical higher-order logic. This provides a uniform framework for computer-assisted assessment of abstract argumentation frameworks using…

Embeddings are a fundamental component of many modern machine learning and natural language processing models. Understanding them and visualizing them is essential for gathering insights about the information they capture and the behavior…

In a recent paper as an alternative to models based on the notion of ideal mathematical point, characterized by a property of separatedness, we considered a viewpoint based on the notion of continuous change, making use of elements of a…

A common representation of a three dimensional object in computer applications, such as graphics and design, is in the form of a triangular mesh. In many instances, individual or groups of triangles in such representation need to satisfy…

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…

Various non-trivial spaces are becoming popular for embedding structured data such as graphs, texts, or images. Following spherical and hyperbolic spaces, more general product spaces have been proposed. However, searching for the best…

The concepts of fuzzy objects and their classes are described that make it possible to structurally represent knowledge about fuzzy and partially-defined objects and their classes. Operations over such objects and classes are also proposed…

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…

Fuzzy sets are the cornerstone of a non-additive uncertainty theory, namely possibility theory, and of a versatile tool for both linguistic and numerical modeling. Numerous works now combine fuzzy concepts with other scientific disciplines…

We introduce an alternative formalization of curved spaces in which the concept of a pointwise affine space, as defined here, replaces that of a manifold. New or modified definitions of familiar notions from differential geometry such as…

A detailed study of graded frame, graded fuzzy topological system and fuzzy topological space with graded inclusion is already done in our earlier paper. The notions of graded fuzzy topological system and fuzzy topological space with graded…

We present ShapeShift, a method for arranging rigid objects into configurations that visually convey semantic concepts specified by natural language. While pretrained diffusion models provide powerful semantic guidance, such as Score…

Automated decision making is often complicated by the complexity of the knowledge involved. Much of this complexity arises from the context sensitive variations of the underlying phenomena. We propose a framework for representing…

This article proposes a new discrete framework for approximating solutions to shape optimization problems under convexity constraints. The numerical method, based on the support function or the gauge function, is guaranteed to generate…

In this paper, we define precompact set in intuitionistic fuzzy metric spaces and prove that any subset of an intuitionistic fuzzy metric space is compact if and only if it is precompact and complete. Also we define topologically complete…

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…

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…

Informally, the 'linear representation hypothesis' is the idea that high-level concepts are represented linearly as directions in some representation space. In this paper, we address two closely related questions: What does "linear…

In this paper a knowledge representation model are proposed, FP5, which combine the ideas from fuzzy sets and penta-valued logic. FP5 represents imprecise properties whose accomplished degree is undefined, contradictory or indeterminate for…

Quantization of spacetime by means of finite dimensional matrices is the basic idea of fuzzy spaces. There remains an issue of quantizing time, however, the idea is simple and it provides an interesting interplay of various ideas in…