Related papers: Categorical Calculus and Algebra for Multi-Model D…
A theory of data types based on category theory is presented. We organize data types under a new categorical notion of F,G-dialgebras which is an extension of the notion of adjunctions as well as that of T-algebras. T-algebras are also used…
Text analytical tasks like word embedding, phrase mining, and topic modeling, are placing increasing demands as well as challenges to existing database management systems. In this paper, we provide a novel algebraic approach based on…
Search engine results pages are usually abstracted as binary relevance vectors and hence are categorical data, meaning that only a limited set of operations is permitted, most notably tabulation of occurrence frequencies, with determination…
We present a system to translate natural language sentences to formulas in a formal or a knowledge representation language. Our system uses two inverse lambda-calculus operators and using them can take as input the semantic representation…
Most graph query languages are rooted in logic. By contrast, in this paper we consider graph query languages rooted in linear algebra. More specifically, we consider MATLANG, a matrix query language recently introduced, in which some basic…
The vocabulary mismatch problem is one of the important challenges facing traditional keyword-based Information Retrieval Systems. The aim of query expansion (QE) is to reduce this query-document mismatch by adding related or synonymous…
We study the expressive power of the LARA language -- a recently proposed unified model for expressing relational and linear algebra operations -- both in terms of traditional database query languages and some analytic tasks often performed…
Fiore and Hur recently introduced a conservative extension of universal algebra and equational logic from first to second order. Second-order universal algebra and second-order equational logic respectively provide a model theory and a…
The number of possible methods of generalizing binary classification to multi-class classification increases exponentially with the number of class labels. Often, the best method of doing so will be highly problem dependent. Here we present…
Database system architectures are undergoing revolutionary changes. Algorithms and data are being unified by integrating programming languages with the database system. This gives an extensible object-relational system where non-procedural…
Natural language interfaces to tabular data must handle ambiguities inherent to queries. Instead of treating ambiguity as a deficiency, we reframe it as a feature of cooperative interaction where users are intentional about the degree to…
With the rising applications implemented in different domains, it is inevitable to require databases to adopt corresponding appropriate data models to store and exchange data derived from various sources. To handle these data models in a…
The categorical models of the differential lambda-calculus are additive categories because of the Leibniz rule which requires the summation of two expressions. This means that, as far as the differential lambda-calculus and differential…
The study of graph queries in database theory has spanned more than three decades, resulting in a multitude of proposals for graph query languages. These languages differ in the mechanisms. We can identify three main families of languages,…
We prove a general congruence result for bisimilarity in higher-order languages, which generalises previous work to languages specified by a labelled transition system in which programs may occur as labels, and which may rely on operations…
As the twin movements of open science and open source bring an ever greater share of the scientific process into the digital realm, new opportunities arise for the meta-scientific study of science itself, including of data science and…
Much work has been done to give semantics to probabilistic programming languages. In recent years, most of the semantics used to reason about probabilistic programs fall in two categories: semantics based on Markov kernels and semantics…
The popularity of data science as a discipline and its importance in the emerging economy and industrial progress dictate that machine learning be democratized for the masses. This also means that the current practice of workforce training…
In this extended abstract we provide a unifying framework that can be used to characterize and compare the expressive power of query languages for different data base models. The framework is based upon the new idea of valid partition, that…
In this paper, we provide a comprehensive rigorous modeling for multidimensional spaces with hierarchically structured dimensions in several layers of abstractions and data cubes that live in such spaces. We model cube queries and their…