Evaluating aggregate functions on possibilistic data

The need for extending information management systems to handle the imprecision of information found in the real world has been recognized. Fuzzy set theory together with possibility theory represent a uniform framework for extending the relational database model with these features. However, none of the existing proposals for handling imprecision in the literature has dealt with queries involving a functional evaluation of a set of items, traditionally referred to as aggregation. Two kinds of aggregate operators, namely, scalar aggregates and aggregate functions, exist. Both are important for most real-world applications, and are thus being supported by traditional languages like SQL or QUEL. This paper presents a framework for handling these two types of aggregates in the context of imprecise information. We consider three cases, specifically, aggregates within vague queries on precise data, aggregates within precisely specified queries on possibilistic data, and aggregates within vague queries on imprecise data. These extensions are based on fuzzy set-theoretical concepts such as the extension principle, the sigma-count operation, and the possibilistic expected value. The consistency and completeness of the proposed operations is shown

From Nested-Loop to Join Queries in OODB

Most declarative SQL-like query languages for object-oriented database systems are orthogonal languages allowing for arbitrary nesting of expressions in the select-, from-, and where-clause. Expressions in the from-clause may be base tables as well as set-valued attributes. In this paper, we propose a general strategy for the optimization of nested OOSQL queries. As in the relational model, the translation/optimization goal is to move from tuple- to set-oriented query processing. Therefore, OOSQL is translated into the algebraic language ADL, and by means of algebraic rewriting nested queries are transformed into join queries as far as possible. Three different optimization options are described, and a strategy to assign priorities to options is proposed

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

High Level Efficiency in Database Languages

The subject of this Ph.D. thesis is the design and implementation of database languages. The thesis consists of five articles:  [1] Joan F. Boyar and Kim S. Larsen. Efficient Rebalancing of Chromatic Search Trees. In O. Nurmi and E. Ukkonen, eds., LNCS 621: Algorithm Theory -- SWAT'92 , pp. 151-164. Springer-Verlag, 1992. [2] Kim S. Larsen. On Aggregation and Computation on Domain Values. PB-414, Computer Science Department, Aarhus University, 1992. [3] Kim S. Larsen. Strategies for Expression Evaluation Using Sort-Merge Algorithms. PB-415, Computer Science Department, Aarhus University, 1992. [4] Kim S. Larsen and Michael I. Schwartzbach. Injectivity of Unary Queries With Computation on Domain Values. Computer Science Department, Aarhus University, 1992. Revised version of PB-311. [5] Kim S. Larsen, Michael I. Schwartzbach and Erik M. Schmidt. A New Formalism for Relational Algebra. IPL , 41(3):163-168, 1992. and this survey paper. In [5], a new query language design is proposed. The expressive power of the language is determined in [2] and all reasonable extensions are considered. In [3, 4], we focus on the optimization issue of avoiding unnecessary sorting of relations. The results in these papers are directly applicable to any algebra-based query language. In addition to the query language part, a database system also has to offer update facilities. The theory of standard tuple based updates is quite well developed in the sequential case. In [1], we discuss a new concurrent implementation of balanced search trees for that purpose.This survey paper describes the results of the papers which form the thesis, and relates these results to each other and to the area in a broader sense than is customary in the introductions of individual papers. The paper is intended to be read in combination with the papers on which it is based

Dmodel and Dalgebra : a data model and algebra for office documents

This dissertation presents a data model (called D_model) and an algebra (called D_ algebra) for office documents. The data model adopts a very natural view of modeling office documents. Documents are grouped into classes; each class is characterized by a frame template , which describes the properties (or attributes) for the class of documents. A frame template is instantiated by providing it with values to form a frame instance which becomes the synopsis of the document of the class associated with the frame template. Different frame instances can be grouped into a folder. Therefore, a folder is a set of frame instances which need not be over the same frame template. The D_model is a dual model which describes documents using two hierarchies: a document type hierarchy which depicts the structural organization of the documents and a folder organization, which represents the user\u27s real-world document filing system. The document type hierarchy exploits structural commonalities between frame templates. Such a hierarchy helps classify various documents. The folder organization mimics the user\u27s real-world document filing system and provides the user with an intuitively clear view of the filing system. This facilitates document retrieval activities. The D_algebra includes a family of operators which together comprise the fundamental query language for the D_model. The algebra provides operators that can be applied to folders which contain frame instances of different types. It has more expressive power than the relational algebra. It extends the classical relational algebra by associating attributes with types, and supporting attribute inheritance. Aggregate operators which can be applied to different frame instances in a folder are also provided. The proposed algebra is used as a sound basis to express the semantics of a high level query language for a document processing system, called TEXPROS. In the model, frame instances can represent incomplete information. Null values of the form value at present unknown are used to denote missing information in some fields of the incomplete frame instances. This dissertation provides a proof-theoretic characterization of the data model and defines the semantics of the null values within the proof-theoretic paradigm