Related papers: Representing Knowledge and Querying Data using Dou…

Modern database systems face a significant challenge in effectively handling the Variety of data. The primary objective of this paper is to establish a unified data model and theoretical framework for multi-model data management. To achieve…

We provide an overview of the hybrid compositional distributional model of meaning, developed in Coecke et al. (arXiv:1003.4394v1 [cs.CL]), which is based on the categorical methods also applied to the analysis of information flow in…

The contribution of this article is a data concept that is essentially based on the two concepts of information and computable functionality. In short, data is viewed as typed information. A data type is defined as a pair of a set of…

Many formal languages of contemporary mathematical music theory -- particularly those employing category theory -- are powerful but cumbersome: ideas that are conceptually simple frequently require expression through elaborate categorical…

There are many category-theoretic notions of algebraic theory, including Lawvere theories, monads, PROPs and operads. The first central notion of this thesis is a common generalisation of these, which we call a proto-theory. In order to…

In this paper we present $2$-category theory from the perspective of Gray-categories using the graphical calculus of separated surface diagrams. As an extended example we consider cones and limits of $2$-functors. Then we use the canonical…

The paper provides a survey of semantic methods for solution of fundamental tasks in mathematical knowledge management. Ontological models and formalisms are discussed. We propose an ontology of mathematical knowledge, covering a wide range…

In a Systems Engineering setting, various models are produced using a variety of methods and tools. Focusing on a type of models -- called descriptive models -- which we shall describe, we argue that, while the clarity and precision of…

Knowledge can be represented compactly in a multitude ways, from a set of propositional formulas, to a Kripke model, to a database. In this paper we study the aggregation of information coming from multiple sources, each source submitting a…

We propose a novel database model whose basic structure is a labeled, directed, acyclic graph with a single root, in which the nodes represent the data sets of an application and the edges represent functional relationships among the data…

Regular logic can be regarded as the internal language of regular categories, but the logic itself is generally not given a categorical treatment. In this paper, we understand the syntax and proof rules of regular logic in terms of the free…

Codd's Theorem, a fundamental result of database theory, asserts that relational algebra and relational calculus have the same expressive power on relational databases. We explore Codd's Theorem for databases over semirings and establish…

Word embeddings have been found to capture a surprisingly rich amount of syntactic and semantic knowledge. However, it is not yet sufficiently well-understood how the relational knowledge that is implicitly encoded in word embeddings can be…

Regular logic can be regarded as the internal language of regular categories, but the logic itself is generally not given a categorical treatment. In this paper, we understand the syntax and proof rules of regular logic in terms of the free…

The cartesian structure possessed by relations, spans, profunctors, and other such morphisms is elegantly expressed by universal properties in double categories. Though cartesian double categories were inspired in part by the older program…

This paper unites two problem-solving traditions in computer science: (1) constraint-based reasoning, and (2) formal concept analysis. For basic definitions and properties of networks of constraints, we follow the foundational approach of…

In this work, we propose a new method to integrate two recent lines of work: unsupervised induction of shallow semantics (e.g., semantic roles) and factorization of relations in text and knowledge bases. Our model consists of two…

The unprecedented pace of machine learning research has lead to incredible advances, but also poses hard challenges. At present, the field lacks strong theoretical underpinnings, and many important achievements stem from ad hoc design…

The fusion of causal models with deep learning introducing increasingly intricate data sets, such as the causal associations within images or between textual components, has surfaced as a focal research area. Nonetheless, the broadening of…

Large language models show human-like performance in knowledge extraction, reasoning and dialogue, but it remains controversial whether this performance is best explained by memorization and pattern matching, or whether it reflects…