ON COMPLETENESS OF HISTORICAL RELATIONAL QUERY LANGUAGES

Numerous proposals for extending the relational data model to incorporate the temporal dimension of data have appeared in the past several years. These proposals have differed considerably in the way that the temporal dimension has been incorporated both into the structure of the extended relations of these temporal models, and consequently into the extended relational algebra or calculus that they define. Because of these differences it has been difficult to compare the proposed models and to make judgments as to which of them might in some sense be equivalent or even better. In this paper we define the notions of temporally grouped and temporally ungrouped historical data models and propose two notions of historical relational completeness, analogous to Codd's notion of relational completeness, one for each type of model. We show that the temporally ungrouped models are less powerful than the grouped models, but demonstrate a technique for extending the ungrouped models with a grouping mechanism to capture the additional semantic power of temporal grouping. For the ungrouped models we define three different languages, a temporal logic, a logic with explicit reference to time, and a temporal algebra, and show that under certain assumptions all three are equivalent in power. For the grouped models we define a many-sorted logic with variables over ordinary values, historical values, and times. Finally, we demonstrate the equivalence of this grouped calculus and the ungrouped calculus extended with the proposed grouping mechanism. We believe the classification of historical data models into grouped and ungrouped provides a useful framework for the comparison of models in the literature, and furthermore the exposition of equivalent languages for each type provides reasonable standards for common, and minimal, notions of historical relational completeness.Information Systems Working Papers Serie

Query processing in temporal object-oriented databases

This PhD thesis is concerned with historical data management in the context of objectoriented databases. An extensible approach has been explored to processing temporal object queries within a uniform query framework. By the uniform framework, we mean temporal queries can be processed within the existing object-oriented framework that is extended from relational framework, by extending the existing query processing techniques and strategies developed for OODBs and RDBs. The unified model of OODBs and RDBs in UmSQL/X has been adopted as a basis for this purpose. A temporal object data model is thereby defined by incorporating a time dimension into this unified model of OODBs and RDBs to form temporal relational-like cubes but with the addition of aggregation and inheritance hierarchies. A query algebra, that accesses objects through these associations of aggregation, inheritance and timereference, is then defined as a general query model /language. Due to the extensive features of our data model and reducibility of the algebra, a layered structure of query processor is presented that provides a uniforrn framework for processing temporal object queries. Within the uniform framework, query transformation is carried out based on a set of transformation rules identified that includes the known relational and object rules plus those pertaining to the time dimension. To evaluate a temporal query involving a path with timereference, a strategy of decomposition is proposed. That is, evaluation of an enhanced path, which is defined to extend a path with time-reference, is decomposed by initially dividing the path into two sub-paths: one containing the time-stamped class that can be optimized by making use of the ordering information of temporal data and another an ordinary sub-path (without time-stamped classes) which can be further decomposed and evaluated using different algorithms. The intermediate results of traversing the two sub-paths are then joined together to create the query output. Algorithms for processing the decomposed query components, i. e., time-related operation algorithms, four join algorithms (nested-loop forward join, sort-merge forward join, nested-loop reverse join and sort-merge reverse join) and their modifications, have been presented with cost analysis and implemented with stream processing techniques using C++. Simulation results are also provided. Both cost analysis and simulation show the effects of time on the query processing algorithms: the join time cost is linearly increased with the expansion in the number of time-epochs (time-dimension in the case of a regular TS). It is also shown that using heuristics that make use of time information can lead to a significant time cost saving. Query processing with incomplete temporal data has also been discussed

On Completeness of Historical Relational Query Languages

Numerous proposals for extending the relational data model to incorporate the temporal dimension of data have appeared in the past several years. These proposals have differed considerably in the way that the temporal dimension has been incorporated both into the structure of the extended relations of these temporal models, and consequently into the extended relational algebra or calculus that they define. Because of these differences it has been difficult to compare the proposed models and to make judgments as to which of them might in some sense be equivalent or even better. In this paper we define the notions of temporally grouped and temporally ungrouped historical data models and propose two notions of historical reIationa1 completeness, analogous to Codd's notion of relational completeness, one for each type of model. We show that the temporally ungrouped models are less expressive than the grouped models, but demonstrate a technique for extending the ungrouped models with a grouping mechanism to capture the additional semantic power of temporal grouping. For the ungrouped models we define three different languages, a temporal logic, a logic with explicit reference to time, and a temporal algebra, and show that under certain assumptions all three are equivalent in power. For the grouped models we define a many-sorted logic with variables over ordinary values, historical values, and times. Finally, we demonstrate the equivalence of this grouped calculus and the ungrouped calculus extended with a grouping mechanism. We believe the classification of historical data models into grouped and ungrouped provides a useful framework for the comparison of models in the literature, and furthermore the exposition of equivalent languages for each type provides reasonable standards for common, and minimal, notions of historical relational completeness.Information Systems Working Papers Serie

Constructing a concept of number

Numbers are concepts whose content, structure, and organization are influenced by the material forms used to represent and manipulate them. Indeed, as argued here, it is the inclusion of multiple forms (distributed objects, fingers, single- and two-dimensional forms like pebbles and abaci, and written notations) that is the mechanism of numerical elaboration. Further, variety in employed forms explains at least part of the synchronic and diachronic variability that exists between and within cultural number systems. Material forms also impart characteristics like linearity that may persist in the form of knowledge and behaviors, ultimately yielding numerical concepts that are irreducible to and functionally independent of any particular form. Material devices used to represent and manipulate numbers also interact with language in ways that reinforce or contrast different aspects of numerical cognition. Not only does this interaction potentially explain some of the unique aspects of numerical language, it suggests that the two are complementary but ultimately distinct means of accessing numerical intuitions and insights. The potential inclusion of materiality in contemporary research in numerical cognition is advocated, both for its explanatory power, as well as its influence on psychological, behavioral, and linguistic aspects of numerical cognition

Mapping Big Data into Knowledge Space with Cognitive Cyber-Infrastructure

Big data research has attracted great attention in science, technology, industry and society. It is developing with the evolving scientific paradigm, the fourth industrial revolution, and the transformational innovation of technologies. However, its nature and fundamental challenge have not been recognized, and its own methodology has not been formed. This paper explores and answers the following questions: What is big data? What are the basic methods for representing, managing and analyzing big data? What is the relationship between big data and knowledge? Can we find a mapping from big data into knowledge space? What kind of infrastructure is required to support not only big data management and analysis but also knowledge discovery, sharing and management? What is the relationship between big data and science paradigm? What is the nature and fundamental challenge of big data computing? A multi-dimensional perspective is presented toward a methodology of big data computing.Comment: 59 page

Efficient Regularized Least-Squares Algorithms for Conditional Ranking on Relational Data

In domains like bioinformatics, information retrieval and social network analysis, one can find learning tasks where the goal consists of inferring a ranking of objects, conditioned on a particular target object. We present a general kernel framework for learning conditional rankings from various types of relational data, where rankings can be conditioned on unseen data objects. We propose efficient algorithms for conditional ranking by optimizing squared regression and ranking loss functions. We show theoretically, that learning with the ranking loss is likely to generalize better than with the regression loss. Further, we prove that symmetry or reciprocity properties of relations can be efficiently enforced in the learned models. Experiments on synthetic and real-world data illustrate that the proposed methods deliver state-of-the-art performance in terms of predictive power and computational efficiency. Moreover, we also show empirically that incorporating symmetry or reciprocity properties can improve the generalization performance