Interoperability in the OpenDreamKit Project: The Math-in-the-Middle Approach

OpenDreamKit --- "Open Digital Research Environment Toolkit for the Advancement of Mathematics" --- is an H2020 EU Research Infrastructure project that aims at supporting, over the period 2015--2019, the ecosystem of open-source mathematical software systems. From that, OpenDreamKit will deliver a flexible toolkit enabling research groups to set up Virtual Research Environments, customised to meet the varied needs of research projects in pure mathematics and applications. An important step in the OpenDreamKit endeavor is to foster the interoperability between a variety of systems, ranging from computer algebra systems over mathematical databases to front-ends. This is the mission of the integration work package (WP6). We report on experiments and future plans with the \emph{Math-in-the-Middle} approach. This information architecture consists in a central mathematical ontology that documents the domain and fixes a joint vocabulary, combined with specifications of the functionalities of the various systems. Interaction between systems can then be enriched by pivoting off this information architecture.Comment: 15 pages, 7 figure

A Programming Environment Evaluation Methodology for Object-Oriented Systems

The object-oriented design strategy as both a problem decomposition and system development paradigm has made impressive inroads into the various areas of the computing sciences. Substantial development productivity improvements have been demonstrated in areas ranging from artificial intelligence to user interface design. However, there has been very little progress in the formal characterization of these productivity improvements and in the identification of the underlying cognitive mechanisms. The development and validation of models and metrics of this sort require large amounts of systematically-gathered structural and productivity data. There has, however, been a notable lack of systematically-gathered information on these development environments. A large part of this problem is attributable to the lack of a systematic programming environment evaluation methodology that is appropriate to the evaluation of object-oriented systems

Constraint capture and maintenance in engineering design

The Designers' Workbench is a system, developed by the Advanced Knowledge Technologies (AKT) consortium to support designers in large organizations, such as Rolls-Royce, to ensure that the design is consistent with the specification for the particular design as well as with the company's design rule book(s). In the principal application discussed here, the evolving design is described against a jet engine ontology. Design rules are expressed as constraints over the domain ontology. Currently, to capture the constraint information, a domain expert (design engineer) has to work with a knowledge engineer to identify the constraints, and it is then the task of the knowledge engineer to encode these into the Workbench's knowledge base (KB). This is an error prone and time consuming task. It is highly desirable to relieve the knowledge engineer of this task, and so we have developed a system, ConEditor+ that enables domain experts themselves to capture and maintain these constraints. Further we hypothesize that in order to appropriately apply, maintain and reuse constraints, it is necessary to understand the underlying assumptions and context in which each constraint is applicable. We refer to them as “application conditions” and these form a part of the rationale associated with the constraint. We propose a methodology to capture the application conditions associated with a constraint and demonstrate that an explicit representation (machine interpretable format) of application conditions (rationales) together with the corresponding constraints and the domain ontology can be used by a machine to support maintenance of constraints. Support for the maintenance of constraints includes detecting inconsistencies, subsumption, redundancy, fusion between constraints and suggesting appropriate refinements. The proposed methodology provides immediate benefits to the designers and hence should encourage them to input the application conditions (rationales)

Topological Equivalence and Similarity in Multi-Representation Geographic Databases

Geographic databases contain collections of spatial data representing the variety of views for the real world at a specific time. Depending on the resolution or scale of the spatial data, spatial objects may have different spatial dimensions, and they may be represented by point, linear, or polygonal features, or combination of them. The diversity of data that are collected over the same area, often from different sources, imposes a question of how to integrate and to keep them consistent in order to provide correct answers for spatial queries. This thesis is concerned with the development of a tool to check topological equivalence and similarity for spatial objects in multi-representation databases. The main question is what are the components of a model to identify topological consistency, based on a set of possible transitions for the different types of spatial representations. This work develops a new formalism to model consistently spatial objects and spatial relations between several objects, each represented at multiple levels of detail. It focuses on the topological consistency constraints that must hold among the different representation of objects, but it is not concerned about generalization operations of how to derive one representation level from another. The result of this thesis is a?computational tool to evaluate topological equivalence and similarity across multiple representations. This thesis proposes to organize a spatial scene -a set of spatial objects and their embeddings in space- directly as a relation-based model that uses a hierarchical graph representation. The focus of the relation-based model is on relevant object representations. Only the highest-dimensional object representations are explicitly stored, while their parts are not represented in the graph

Formal design of data warehouse and OLAP systems : a dissertation presented in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Information Systems at Massey University, Palmerston North, New Zealand

A data warehouse is a single data store, where data from multiple data sources is integrated for online business analytical processing (OLAP) of an entire organisation. The rationale being single and integrated is to ensure a consistent view of the organisational business performance independent from different angels of business perspectives. Due to its wide coverage of subjects, data warehouse design is a highly complex, lengthy and error-prone process. Furthermore, the business analytical tasks change over time, which results in changes in the requirements for the OLAP systems. Thus, data warehouse and OLAP systems are rather dynamic and the design process is continuous. In this thesis, we propose a method that is integrated, formal and application-tailored to overcome the complexity problem, deal with the system dynamics, improve the quality of the system and the chance of success. Our method comprises three important parts: the general ASMs method with types, the application tailored design framework for data warehouse and OLAP, and the schema integration method with a set of provably correct refinement rules. By using the ASM method, we are able to model both data and operations in a uniform conceptual framework, which enables us to design an integrated approach for data warehouse and OLAP design. The freedom given by the ASM method allows us to model the system at an abstract level that is easy to understand for both users and designers. More specifically, the language allows us to use the terms from the user domain not biased by the terms used in computer systems. The pseudo-code like transition rules, which gives the simplest form of operational semantics in ASMs, give the closeness to programming languages for designers to understand. Furthermore, these rules are rooted in mathematics to assist in improving the quality of the system design. By extending the ASMs with types, the modelling language is tailored for data warehouse with the terms that are well developed for data-intensive applications, which makes it easy to model the schema evolution as refinements in the dynamic data warehouse design. By providing the application-tailored design framework, we break down the design complexity by business processes (also called subjects in data warehousing) and design concerns. By designing the data warehouse by subjects, our method resembles Kimball's "bottom-up" approach. However, with the schema integration method, our method resolves the stovepipe issue of the approach. By building up a data warehouse iteratively in an integrated framework, our method not only results in an integrated data warehouse, but also resolves the issues of complexity and delayed ROI (Return On Investment) in Inmon's "top-down" approach. By dealing with the user change requests in the same way as new subjects, and modelling data and operations explicitly in a three-tier architecture, namely the data sources, the data warehouse and the OLAP (online Analytical Processing), our method facilitates dynamic design with system integrity. By introducing a notion of refinement specific to schema evolution, namely schema refinement, for capturing the notion of schema dominance in schema integration, we are able to build a set of correctness-proven refinement rules. By providing the set of refinement rules, we simplify the designers's work in correctness design verification. Nevertheless, we do not aim for a complete set due to the fact that there are many different ways for schema integration, and neither a prescribed way of integration to allow designer favored design. Furthermore, given its °exibility in the process, our method can be extended for new emerging design issues easily

Cartographic Generalization in Digital Environment

Throughout the world numerous efforts to automate generalization are in progress. The results are yet to be satisfactory. Ample reasoning can be given to justify the lack of success, the most important being that generalization is an ambiguous process, highly subjective which lacks definitive rules, guidelines or systematization. This paper deals with the problem of generalization of vector data bases through the analysis of recent developments and research in the field. These developments tend to establish a promising framework which, with subsequent refinements and the utilization of state-of-the-art computer technology, may lead to successful results. What is needed is what lacks: Definitive rules in structuring the digital image of the world and development of expert systems which will intelligently manipulate this image

Interoperability in the OpenDreamKit project : the Math-in-the-Middle approach

OpenDreamKit - "Open Digital Research Environment Toolkit for the Advancement of Mathematics" - is an H2020 EU Research Infrastructure project that aims at supporting, over the period 2015-2019, the ecosystem of open-source mathematical software systems. OpenDreamKit will deliver a flexible toolkit enabling research groups to set up Virtual Research Environments, customised to meet the varied needs of research projects in pure mathematics and applications. An important step in the OpenDreamKit endeavor is to foster the interoperability between a variety of systems, ranging from computer algebra systems over mathematical databases to front-ends. This is the mission of the integration work package. We report on experiments and future plans with the Math-in-the-Middle approach. This architecture consists of a central mathematical ontology that documents the domain and xes a joint vocabulary, or even a language, going beyond existing systems such as OpenMath, combined with specifications of the functionalities of the various systems. Interaction between systems can then be enriched by pivoting around this architecture.Postprin