Related papers: Relational Algebra and Calculus with SQL Null Valu…
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…
The relational data model requires a theory of relations in which tuples are not only many-sorted, but can also have indexes that are not necessarily numerical. In this paper we develop such a theory and define operations on relations that…
We present a survey of existing approaches to relational division in rank-aware databases, discuss issues of the present approaches, and outline generalizations of several types of classic division-like operations. We work in a model which…
The design of SQL is based on a three-valued logic (3VL), rather than the familiar Boolean logic. 3VL adds a truth value unknown to true and false to handle nulls. Viewed as indispensable for SQL expressiveness, it is at the same time much…
SQL is the world's most popular declarative language, forming the basis of the multi-billion-dollar database industry. Although SQL has been standardized, the full standard is based on ambiguous natural language rather than formal…
The Nested Relational Calculus (NRC) has been an influential high-level query language, providing power and flexibility while still allowing translation to standard SQL queries. It has also been used as a basis for language-integrated query…
Queries with aggregation and arithmetic operations, as well as incomplete data, are common in real-world database, but we lack a good understanding of how they should interact. On the one hand, systems based on SQL provide ad-hoc rules for…
Since the inception of SQL, nulls have frustrated database users and builders alike. Those writing SQL must painstakingly guard their queries against surprising results caused by nulls, while those building database engines constantly…
We present a number of first- and second-order extensions to SMT theories specifically aimed at representing and analyzing SQL queries with join, projection, and selection operations. We support reasoning about SQL queries with either bag…
Financial transactions, internet search, and data analysis are all placing increasing demands on databases. SQL, NoSQL, and NewSQL databases have been developed to meet these demands and each offers unique benefits. SQL, NoSQL, and NewSQL…
This paper concerns an expansion of first-order Belnap-Dunn logic, named $\mathrm{BD}^{\supset,\mathsf{F}}$, and an application of this logic in the area of relational database theory. The notion of a relational database, the notion of a…
This paper analyzes the fatal drawback of the relational calculus not allowing relations to be domains of relations, and its consequences entrenched in SQL. In order to overcome this obstacle we propose "multitable index" - an easily…
The position we advocate in this paper is that relational algebra can provide a unified language for both representing and computing with statistical-relational objects, much as linear algebra does for traditional single-table machine…
The meaning of null in relational databases is a major source of confusion not only among database users but also among database textbook writers. The purpose of this article is to examine what database nulls could mean and to make some…
We present sensitivity analysis for results of query executions in a relational model of data extended by ordinal ranks. The underlying model of data results from the ordinary Codd's model of data in which we consider ordinal ranks of…
The database community lacks a unified relational query language for subset selection and optimisation queries, limiting both user expression and query optimiser reasoning about such problems. Decades of research (latterly under the rubric…
We study the complexity of various fundamental counting problems that arise in the context of incomplete databases, i.e., relational databases that can contain unknown values in the form of labeled nulls. Specifically, we assume that the…
A significant category of NoSQL approaches is known as graph da-tabases. They are usually represented by one property graph. We introduce a functional approach to modelling relations and property graphs. Single-valued and multivalued…
We propose a new formalism for specifying and reasoning about problems that involve heterogeneous "pieces of information" -- large collections of data, decision procedures of any kind and complexity and connections between them. The essence…
This paper is about Kripke structures that are inside a relational database and queried with a modal language. At first the modal language that is used is introduced, followed by a definition of the database and relational algebra. Based on…