Disjunctively incomplete information in relational databases: modeling and related issues

In this dissertation, the issues related to the information incompleteness in relational databases are explored. In general, this dissertation can be divided into two parts. The first part extends the relational natural join operator and the update operations of insertion and deletion to I-tables, an extended relational model representing inclusively indefinite and maybe information, in a semantically correct manner. Rudimentary or naive algorithms for computing natural joins on I-tables require an exponential number of pair-up operations and block accesses proportional to the size of I-tables due to the combinatorial nature of natural joins on I-tables. Thus, the problem becomes intractable for large I-tables. An algorithm for computing natural joins under the extended model which reduces the number of pair-up operations to a linear order of complexity in general and in the worst case to a polynomial order of complexity with respect to the size of I-tables is proposed in this dissertation. In addition, this algorithm also reduces the number of block accesses to a linear order of complexity with respect to the size of I-tables;The second part is related to the modeling aspect of incomplete databases. An extended relational model, called E-table, is proposed. E-table is capable of representing exclusively disjunctive information. That is, disjunctions of the form P[subscript]1\mid P[subscript]2\mid·s\mid P[subscript]n, where ǁ denotes a generalized logical exclusive or indicating that exactly one of the P[subscript]i\u27s can be true. The information content of an E-table is precisely defined and relational operators of selection, projection, difference, union, intersection, and cartisian product are extended to E-tables in a semantically correct manner. Conditions under which redundancies could arise due to the presence of exclusively disjunctive information are characterized and the procedure for resolving redundancies is presented;Finally, this dissertation is concluded with discussions on the directions for further research in the area of incomplete information modeling. In particular, a sketch of a relational model, IE-table (Inclusive and Exclusive table), for representing both inclusively and exclusively disjunctive information is provided

Inconsistency and Incompleteness in Relational Databases and Logic Programs

The aim of this thesis is to study the role played by negation in databases and to develop data models that can handle inconsistent and incomplete information. We develop models that also allow incompleteness through disjunctive information under both the CWA and the OWA in relational databases. In the area of logic programming, extended logic programs allow explicit representation of negative information. As a result, a number of extended logic programs have an inconsistent semantics. We present a translation of extended logic programs to normal logic programs that is more tolerant to inconsistencies. Extended logic programs have also been used widely in order to compute the repairs of an inconsistent database. We present some preliminary ideas on how source information can be incorporated into the repair program in order to produce a subset of the set of all repairs based on a preference for certain sources over others

Treatment of imprecision in data repositories with the aid of KNOLAP

Traditional data repositories introduced for the needs of business processing, typically focus on the storage and querying of crisp domains of data. As a result, current commercial data repositories have no facilities for either storing or querying imprecise/ approximate data. No significant attempt has been made for a generic and applicationindependent representation of value imprecision mainly as a property of axes of analysis and also as part of dynamic environment, where potential users may wish to define their “own” axes of analysis for querying either precise or imprecise facts. In such cases, measured values and facts are characterised by descriptive values drawn from a number of dimensions, whereas values of a dimension are organised as hierarchical levels. A solution named H-IFS is presented that allows the representation of flexible hierarchies as part of the dimension structures. An extended multidimensional model named IF-Cube is put forward, which allows the representation of imprecision in facts and dimensions and answering of queries based on imprecise hierarchical preferences. Based on the H-IFS and IF-Cube concepts, a post relational OLAP environment is delivered, the implementation of which is DBMS independent and its performance solely dependent on the underlying DBMS engine

Monotonically improving approximate answers to relational algebra queries

We present here a query processing method that produces approximate answers to queries posed in standard relational algebra. This method is monotone in the sense that the accuracy of the approximate result improves with the amount of time spent producing the result. This strategy enables us to trade the time to produce the result for the accuracy of the result. An approximate relational model that characterizes appromimate relations and a partial order for comparing them is developed. Relational operators which operate on and return approximate relations are defined

Disjunctive deductive databases.

by Hwang Hoi Yee Cothan.Thesis (M.Phil.)--Chinese University of Hong Kong, 1996.Includes bibliographical references (leaves 68-70).Abstract --- p.iiAcknowledgement --- p.iiiChapter 1 --- Introduction --- p.1Chapter 1.1 --- Objectives of the Thesis --- p.1Chapter 1.2 --- Overview of the Thesis --- p.7Chapter 2 --- Background and Related Work --- p.8Chapter 2.1 --- Deductive Databases --- p.8Chapter 2.2 --- Disjunctive Deductive Databases --- p.10Chapter 2.3 --- Model tree for disjunctive deductive databases --- p.11Chapter 3 --- Preliminary --- p.13Chapter 3.1 --- Disjunctive Logic Program --- p.13Chapter 3.2 --- Data-disjunctive Logic Program --- p.14Chapter 4 --- Semantics of Data-disjunctive Logic Program --- p.17Chapter 4.1 --- Model-theoretic semantics --- p.17Chapter 4.2 --- Fixpoint semantics --- p.20Chapter 4.2.1 --- Fixpoint operators corresponding to the MMSpDD --- p.22Chapter 4.2.2 --- "Fixpoint operator corresponding to the contingency model, CMP" --- p.25Chapter 4.3 --- Equivalence between the model-theoretic and fixpoint semantics --- p.26Chapter 4.4 --- Operational Semantics --- p.30Chapter 4.5 --- Correspondence with the I-table --- p.31Chapter 5 --- Disjunctive Deductive Databases --- p.33Chapter 5.1 --- Disjunctions in deductive databases --- p.33Chapter 5.2 --- Relation between predicates --- p.35Chapter 5.3 --- Transformation of Disjunctive Deductive Data-bases --- p.38Chapter 5.4 --- Query answering for Disjunctive Deductive Data-bases --- p.40Chapter 6 --- Magic for Data-disjunctive Deductive Database --- p.44Chapter 6.1 --- Magic for Relevant Answer Set --- p.44Chapter 6.1.1 --- Rule rewriting algorithm --- p.46Chapter 6.1.2 --- Bottom-up evaluation --- p.49Chapter 6.1.3 --- Examples --- p.49Chapter 6.1.4 --- Discussion on the rewriting algorithm --- p.52Chapter 6.2 --- Alternative algorithm for Traditional Answer Set --- p.54Chapter 6.2.1 --- Rule rewriting algorithm --- p.54Chapter 6.2.2 --- Examples --- p.55Chapter 6.3 --- Contingency answer set --- p.56Chapter 7 --- Experiments and Comparison --- p.57Chapter 7.1 --- Experimental Results --- p.57Chapter 7.1.1 --- Results for the Traditional answer set --- p.58Chapter 7.1.2 --- Results for the Relevant answer set --- p.61Chapter 7.2 --- Comparison with the evaluation method for Model tree --- p.63Chapter 8 --- Conclusions and Future Work --- p.66Bibliography --- p.6