The GMD Data Model and Algebra for Multidimensional Information (original) (raw)

The GMD Data Model for Multidimensional Information: A Brief Introduction

2003

In this paper we introduce a novel data model for multidimensional information, GMD, generalising the MD data model first proposed in Cabibbo et al (EDBT-98). The aim of this work is not to propose yet another multidimensional data model, but to find the general precise formalism encompassing all the proposals for a logical data model in the data warehouse field. Our proposal is compatible with all these proposals, making therefore possible a formal comparison of the differences of the models in the literature, and to study formal properties or extensions of such data models. Starting with a logic-based definition of the semantics of the GMD data model and of the basic algebraic operations over it, we show how the most important approaches in DW modelling can be captured by it. The star and the snowflake schemas, Gray’s cube, Agrawal’s and Vassiliadis’ models, MD and other multidimensional conceptual data can be captured uniformly by GMD. In this way it is possible to formally understand the real differences in expressivity of the various models, their limits, and their potentials.

A Conceptual Model for Multidimensional Data

2008

This paper introduces a Conceptual Data Model for Data Warehouse including multidimensional aggregation. It is based on Entity-Relationships data model. The conceptual data model gracefully extends standard Entity-Relationship data model with multidimensional aggregated entities. The model has a clear mathematical theoretic semantics grounded on standard ER semantics and the GMD logic-based multidimensional data model. The aim of this work is not to propose yet another conceptual data model, but to find the most general and precise formalism considering all the proposals for a conceptual data model in the data warehouse field, making therefore a possible formal comparison of the differences of the models in the literature, and to study the formal properties or extensions of such data models.

The Ontological Multidimensional Data Model

ArXiv, 2017

In this extended abstract we describe, mainly by examples, the main elements of the Ontological Multidimensional Data Model, which considerably extends a relational reconstruction of the multidimensional data model proposed by Hurtado and Mendelzon by means of tuple-generating dependencies, equality-generating dependencies, and negative constraints as found in Datalog+-. We briefly mention some good computational properties of the model.

Multidimensional models meet the semantic web

Proceedings of the fifteenth international workshop on Data warehousing and OLAP - DOLAP '12, 2012

Data warehouses use a multidimensional model. Based on this model, OLAP cubes enable users to analyze data. For correct OLAP analysis, multidimensional models should be checked. In particular, these models should ensure summarizability. Checking multidimensional models and their summarizability is complex and error-prone. To perform this task, formal reasoning is appropriate. In this paper, we propose and illustrate an approach to represent a multidimensional model as an OWL-DL ontology, and reason on this ontology to check the multidimensional model and its summarizability. Beyond the reasoning capabilities of description logic, representing multidimensional models as OWL-DL ontologies is a means to move multidimensional modeling to the semantic Web. To illustrate this, we investigate the complementarities between our approach and the RDF Data Cube vocabulary, and suggest how they could be combined.

Semantics of data bases: The semantics of data models

Information Systems, 1978

The definition of data equivalence depends on a notion of the semantics (i.e. the meaning) of the data stored in a data base. To define the semantics of these data it is very important to distinguish between the things to be modelled in a data base and the language in which they are represented. We introduce an abstract data model which is suited to express the semantics of schemas respectively data instances. To represent this model we propose a logical data definition language (LDDL) and a logical data language (LDL) which as a consequence allow to specify the kind of information which may bc stored in the data base and which ensures the correctness and consistency of this information.

Towards an Ontology of Multidimensional Data Structures for Analytical Purposes

Hawaii International Conference on System Sciences, 2010

Multidimensional data are the foundation for OLAP applications. They can be provided in several ways: relational OLAP, multidimensional OLAP, or hybrid OLAP. The usage of the underlying technology, which is well understood and in most cases formally defined, does not resolve the issue of a missing vocabulary for multidimensional data on a conceptual level. Some basic definitions are broadly used;

A Formal Algebra for OLAP

ArXiv, 2016

Online Analytical Processing (OLAP) comprises tools and algorithms that allow querying multidimensional databases. It is based on the multidimensional model, where data can be seen as a cube, where each cell contains one or more measures can be aggregated along dimensions. Despite the extensive corpus of work in the field, a standard language for OLAP is still needed, since there is no well-defined, accepted semantics, for many of the usual OLAP operations. In this paper, we address this problem, and present a set of operations for manipulating a data cube. We clearly define the semantics of these operations, and prove that they can be composed, yielding a language powerful enough to express complex OLAP queries. We express these operations as a sequence of atomic transformations over a fixed multidimensional matrix, whose cells contain a sequence of measures. Each atomic transformation produces a new measure. When a sequence of transformations defines an OLAP operation, a flag is p...

Conceptual multidimensional data model based on object-oriented metacube

In this paper, we propose a conceptual multidimensional data model that facilitates a precise rigorous conceptualization for OLAP. First, our approach has strong relation with mathematics by applying a new defined concept, i.e. H-set. Afterwards, the mathematic soundness provides a foundation to handle natural hierarchical relationships among data elements within dimensions with many levels of complexity in their structures. Hereafter, the multidimensional data model organizes data in the form of metacubes, the concept of which is a generalization of other cube models. In addition, a metacube is associated with a set of groups each of which contains a subset of the metacube domain, which is a H-set of data cells. Furthermore, metacube operators (e.g. jumping, rollingUp and drillingDown) are defined in a very elegant manner.

MultiDimensional Logic Programming: Theoretical Foundations

Theoretical Computer Science, 1997

This paper introduces an extension of logic programming based on multi-dimensional logics, called MLP. In a multi-dimensional logic the values of elements vary depending on more than one dimension, such as time and space. The resulting logic programming language is suitable for modelling objects which involve implicit and/or explicit temporal and spatial dependencies. The execution of programs of the language is based on a resolution-type proof procedure called MSLD-resolution (for multi-dimensional SLD-resolution). The paper also establishes the declarative semantics of multi-dimensional logic programs, based on an extension of Herbrand models. In particular, it is shown that MLP programs satisfy the minimum model semantics. A novel multidimensional interface to MLP is also outlined; it can be used as a powerful development tool with the advantage of non-determinism inherent in logic programming.