User Defined Types and Nested Tables in Object Relational Databases

Bernadette Byrne, Mary Garvey, ‘User Defined Types and Nested Tables in Object Relational Databases’, paper presented at the United Kingdom Academy for Information Systems 2006: Putting Theory into Practice, Cheltenham, UK, 5-7 June, 2006.There has been much research and work into incorporating objects into databases with a number of object databases being developed in the 1980s and 1990s. During the 1990s the concept of object relational databases became popular, with object extensions to the relational model. As a result, several relational databases have added such extensions. There has been little in the way of formal evaluation of object relational extensions to commercial database systems. In this work an airline flight logging system, a real-world database application, was taken and a database developed using a regular relational database and again using object relational extensions, allowing the evaluation of the relational extensions.Peer reviewe

A multi-set extended relational algebra: a formal approach to a practical issue

The relational data model is based on sets of tuples, i.e. it does not allow duplicate tuples an a relation. Many database languages and systems do require multi-set semantics though, either because of functional requirements or because of the high costs of duplicate removal in database operations. Several proposals have been presented that discuss multi-set semantics. As these proposals tend to be either rather practical, lacking the formal background, or rather formal, lacking the connection to database practice, the gap between theory and practice has not been spanned yet. This paper proposes a complete extended relational algebra with multi-set semantics, having a clear formal background and a close connection to the standard relational algebra. It includes constructs that extend the algebra to a complete sequential database manipulation language that can either be used as a formal background to other multi-set languages like SQL, or as a database manipulation language on its own. The practical usability of the latter option has been demonstrated in the PRISMA/DB database project, where a variant of the language has been used as the primary database languag

The equational theory of the natural join and inner union is decidable

The natural join and the inner union operations combine relations of a database. Tropashko and Spight [24] realized that these two operations are the meet and join operations in a class of lattices, known by now as the relational lattices. They proposed then lattice theory as an algebraic approach to the theory of databases, alternative to the relational algebra. Previous works [17, 22] proved that the quasiequational theory of these lattices-that is, the set of definite Horn sentences valid in all the relational lattices-is undecidable, even when the signature is restricted to the pure lattice signature. We prove here that the equational theory of relational lattices is decidable. That, is we provide an algorithm to decide if two lattice theoretic terms t, s are made equal under all intepretations in some relational lattice. We achieve this goal by showing that if an inclusion t $\le$ s fails in any of these lattices, then it fails in a relational lattice whose size is bound by a triple exponential function of the sizes of t and s.Comment: arXiv admin note: text overlap with arXiv:1607.0298

Functional dependencies for XML : axiomatisation and normal form in the presence of frequencies and identifiers : a thesis presented in partial fulfilment of the requirements for the degree of Master of Sciences in Information Sciences at Massey University, Palmerston North, New Zealand

XML has gained popularity as a markup language for publishing and exchanging data on the web. Nowadays, there are also ongoing interests in using XML for representing and actually storing data. In particular, much effort has been directed towards turning XML into a real data model by improving the semantics that can be expressed about XML documents. Various works have addressed how to define different classes of integrity constraints and the development of a normalisation theory for XML. One area which received little to no attention from the research community up to five years ago is the study of functional dependencies in the context of XML [37]. Since then, there has been increasingly more research investigating functional dependencies in XML. Nevertheless, a comprehensive dependency theory and normalisation theory for XML have yet to emerge. Functional dependencies are an integral part of database theory in the relational data model (RDM). In particular, functional dependencies have been vital in the investigation of how to design "good" relational database schemas which avoid or minimise problems relating to data redundancy and data inconsistency. Since the same problems can be shown to exist in poorly designed XML schemas 1 , there is a need to investigate how these problems can be eliminated in the context of XML. We believe that the study of an analogy to relational functional dependencies in the context of XML is equally significant towards designing "good" XML schemas. [FROM INTRODUCTION

Extending the relational model with uncertainty and ignorance

It has been widely recognized that in many real-life database applications there is growing demand to model uncertainty and ignorance. However the relational model does not provide this possibility. Through the years a number of efforts has been devoted to the capture of uncertainty and ignorance in databases. Most of these efforts attempted to capture uncertainty using the classic probability theory. As a consequence, the limitations of probability theory are inherited by these approaches, such as the problem of information loss. In this paper, we extend the relational model with uncertainty and ignorance without these limitations posed by the other approaches. Our approach is based on the so-called theory of belief functions, which may be considered as a generalization of probability theory. Belief functions have an attractive mathematical\ud underpinning and many intuitively appealing properties