Related papers: Formal Ways for Measuring Relations between Concep…
Definitions and notations with historical references are given for some numerical coefficients commonly used to quantify relations among collections of objects for the purpose of expressing approximate knowledge and probabilistic reasoning.
This paper introduces a category theory-based framework to redefine physical computing in light of advancements in quantum computing and non-standard computing systems. By integrating classical definitions within this broader perspective,…
Different types of two- and three-dimensional representations of a finite metric space are studied that focus on the accurate representation of the linear order among the distances rather than their actual values. Lower and upper bounds for…
In context of efforts of composing category-theoretic and logical methods in the area of knowledge representation we propose the notion of conceptory. We consider intersection/union and other constructions in conceptories as expressive…
While previous linguistic and psycholinguistic research on space has mainly analyzed spatial relations, the studies reported in this paper focus on how language distinguishes among spatial entities. Descriptive and experimental studies…
This article combines the vocabulary of semiotics and category theory to provide a formal analysis of visualization. It shows how familiar processes of visualization fit the semiotic frameworks of both Saussure and Peirce, and extends these…
Complex systems have become a popular lens for analyzing cities and complexity theory has many implications for urban performance and resilience. This paper develops a typology of measures and indicators for assessing the physical…
Cognitive neuroscience methods can identify the fMRI-measured neural representation of familiar individual concepts, such as apple, and decompose them into meaningful neural and semantic components. This approach was applied here to…
Scientific discovery is a cumulative process and requires new ideas to be situated within an ever-expanding landscape of existing knowledge. An emerging and critical challenge is how to identify conceptually relevant prior work from rapidly…
From antiquity the conceptual perception of space changed painfully and at a relatively slow pace. It went through mythological descriptions, religious beliefs, metaphysical worldviews and cosmological models with a mechanistic structure,…
We provide an overview of a canonical formalism that describes mixed quantum-classical systems in terms of statistical ensembles on configuration space, and discuss applications to measurement theory. It is shown that the formalism allows a…
There are versions of "calculus" in many settings, with various mixtures of algebra and analysis. In these informal notes we consider a few examples that suggest a lot of interesting questions.
Convex sets appear in various mathematical theories, and are used to define notions such as convex functions and hulls. As an abstraction from the usual definition of convex sets in vector spaces, we formalize in Coq an intrinsic…
Quotients and comprehension are fundamental mathematical constructions that can be described via adjunctions in categorical logic. This paper reveals that quotients and comprehension are related to measurement, not only in quantum logic,…
Mathematical notation makes up a large portion of STEM literature, yet finding semantic representations for formulae remains a challenging problem. Because mathematical notation is precise, and its meaning changes significantly with small…
Lexical Semantics is concerned with how words encode mental representations of the world, i.e., concepts . We call this type of concepts, classification concepts . In this paper, we focus on Visual Semantics , namely on how humans build…
Semantic representations can be framed as a structured, dynamic knowledge space through which humans navigate to retrieve and manipulate meaning. To investigate how humans traverse this geometry, we introduce a framework that represents…
Historical linguists have identified multiple forms of lexical semantic change. We present a three-dimensional framework for integrating these forms and a unified computational methodology for evaluating them concurrently. The dimensions…
The purpose of this article is to introduce and motivate the notion of Minkowski (or box) dimension for measures. The definition is simple and fills a gap in the existing literature on the dimension theory of measures. As the terminology…
Advances in word representations have shown tremendous improvements in downstream NLP tasks, but lack semantic interpretability. In this paper, we introduce Definition Frames (DF), a matrix distributed representation extracted from…