Related papers: Interacting Conceptual Spaces
We assume that substances in the world are represented by two types of concepts, namely substance concepts and classification concepts, the former instrumental to (visual) perception, the latter to (language based) classification. Based on…
Hierarchies allow feature sharing between objects at multiple levels of representation, can code exponential variability in a very compact way and enable fast inference. This makes them potentially suitable for learning and recognizing a…
Conceptual combination performs a fundamental role in creating the broad range of compound phrases utilized in everyday language. This article provides a novel probabilistic framework for assessing whether the semantics of conceptual…
The paper introduces a novel framework based on category theory to enhance the explainability of artificial intelligence systems, particularly focusing on word embeddings. Key topics include the construction of categories $\mathcal{L}_T$…
The human brain possesses the extraordinary capability to contextualize the information it receives from our environment. The entorhinal-hippocampal plays a critical role in this function, as it is deeply engaged in memory processing and…
Revealing the implicit semantic relation between the constituents of a noun-compound is important for many NLP applications. It has been addressed in the literature either as a classification task to a set of pre-defined relations or by…
The aim of this paper is twofold: first we will use vector space distributional compositional categorical models of meaning to compare the meaning of sentences in Irish and in English (and thus ascertain when a sentence is the translation…
Due to their versatility, concept maps are used in various educational settings and serve as tools that enable educators to comprehend students' knowledge construction. An essential component for analyzing a concept map is its structure,…
According to the principle of compositional generalization, the meaning of a complex expression can be understood as a function of the meaning of its parts and of how they are combined. This principle is crucial for human language…
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…
Using ideas from synthetic topology, a new approach to descriptive set theory is suggested. Synthetic descriptive set theory promises elegant explanations for various phenomena in both classic and effective descriptive set theory.…
The categorical compositional distributional model of Coecke, Sadrzadeh and Clark provides a linguistically motivated procedure for computing the meaning of a sentence as a function of the distributional meaning of the words therein. The…
The functional approach to compositional distributional semantics considers transitive verbs to be linear maps that transform the distributional vectors representing nouns into a vector representing a sentence. We conduct an initial…
We develop a theory of rewriting for structured cospans in order to extend compositional methods for modeling open networks. First, we introduce a category whose objects are structured cospans, and establish conditions under which it is…
We propose a computationally efficient and high-performance classification algorithm by incorporating class structural information in analysis dictionary learning. To achieve more consistent classification, we associate a class…
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…
In both quantum mechanics and corpus linguistics based on vector spaces, the notion of entanglement provides a means for the various subsystems to communicate with each other. In this paper we examine a number of implementations of the…
The categorical compositional distributional (DisCoCat) model of meaning developed by Coecke et al. (2010) has been successful in modeling various aspects of meaning. However, it fails to model the fact that language can change. We give an…
Psychology has had difficulty accounting for the creative, context-sensitive manner in which concepts are used. We believe this stems from the view of concepts as identifiers rather than bridges between mind and world that participate in…
This is a collection of introductory, expository notes on applied category theory, inspired by the 2018 Applied Category Theory Workshop, and in these notes we take a leisurely stroll through two themes (functorial semantics and…