Safety, Absoluteness, and Computability

The semantic notion of dependent safety is a common generalization of the notion of absoluteness used in set theory and the notion of domain independence used in database theory for characterizing safe queries. This notion has been used in previous works to provide a unified theory of constructions and operations as they are used in different branches of mathematics and computer science, including set theory, computability theory, and database theory. In this paper we provide a complete syntactic characterization of general first-order dependent safety. We also show that this syntactic safety relation can be used for characterizing the set of strictly decidable relations on the natural numbers, as well as for characterizing rudimentary set theory and absoluteness of formulas within it

On derived dependencies and connected databases

AbstractThis paper introduces a new class of deductive databases (connected databases) for which SLDNF-resolution never flounders and always computes ground answers. The class of connected databases properly includes that of allowed databases. Moreover the definition of connected databases enables evaluable predicates to be included in a uniform way. An algorithm is described which, for each predicate defined in a normal database, derives a propositional formula (groundness formula) describing dependencies between the arguments of that predicate. Groundness formulae are used to determine whether a database is connected. They are also used to identify goals for which SLDNF-resolution will never flounder and will always compute ground answers on a connected database

Domain-independent queries on databases with external functions

AbstractWe study queries over databases with external functions, from a language-independent perspective. The input and output types of the external functions can be atomic values, flat relations, nested relations, etc. We propose a new notion of data-independence for queries on databases with external functions, which extends naturally the notion of generic queries on relational databases without external functions. In contrast to previous such notions, ours can also be applied to queries expressed in query languages with iterations. Next, we propose two natural notions of computability for queries over databases with external functions, and prove that they are equivalent, under reasonable assumptions. Thus, our definition of computability is robust. Finally, based on this equivalence result, we give examples of complete query languages with external functions. A byproduct of the equivalence result is the fact that Relational Machines (Abiteboul and V. Vianu, 1991; Abiteboul et al., 1992) are complete on nested relations: they are known not to be complete on flat relations

Distributed Abductive Reasoning: Theory, Implementation and Application

Abductive reasoning is a powerful logic inference mechanism that allows assumptions to be made during answer computation for a query, and thus is suitable for reasoning over incomplete knowledge. Multi-agent hypothetical reasoning is the application of abduction in a distributed setting, where each computational agent has its local knowledge representing partial world and the union of all agents' knowledge is still incomplete. It is different from simple distributed query processing because the assumptions made by the agents must also be consistent with global constraints. Multi-agent hypothetical reasoning has many potential applications, such as collaborative planning and scheduling, distributed diagnosis and cognitive perception. Many of these applications require the representation of arithmetic constraints in their problem specifications as well as constraint satisfaction support during the computation. In addition, some applications may have confidentiality concerns as restrictions on the information that can be exchanged between the agents during their collaboration. Although a limited number of distributed abductive systems have been developed, none of them is generic enough to support the above requirements. In this thesis we develop, in the spirit of Logic Programming, a generic and extensible distributed abductive system that has the potential to target a wide range of distributed problem solving applications. The underlying distributed inference algorithm incorporates constraint satisfaction and allows non-ground conditional answers to be computed. Its soundness and completeness have been proved. The algorithm is customisable in that different inference and coordination strategies (such as goal selection and agent selection strategies) can be adopted while maintaining correctness. A customisation that supports confidentiality during problem solving has been developed, and is used in application domains such as distributed security policy analysis. Finally, for evaluation purposes, a flexible experimental environment has been built for automatically generating different classes of distributed abductive constraint logic programs. This environment has been used to conduct empirical investigation of the performance of the customised system

Query translation and optimisation for complex value databases

This thesis considers the theory of database queries on the complex value data model extended with external functions. In modern intelligent database systems, we expect that query systems be able to handle a wide range of calculus formulas correctly and efficiently. Accordingly, they will require general query translators and efficient optimisers. Motivated by these concerns, this thesis undertakes a· comprehensive study of query evaluation in the complex value model and investigates the following issues: • identifying recursive sets of complex value formulas which define domain independent queries; • implementing complex value calculus queries with the incorporation of functions; • solving the problem of how to process join operation in complex value databases; and • investigating some algebraic properties concerning nested relational operators. The first part of this thesis extends some classical properties of the relational theory - particularly those related to query safety - to the context of complex value databases with fixed external functions and investigates the problem of how to implement calculus queries. Two notions of syntactic criteria for queries which guarantee domain independence, namely, embedded evaluable and embedded allowed, are generalised for this data model. This thesis shows that all embedded-allowed calculus (or fix-point) queries are external-function domain independent and continuous. This thesis discusses the topic of "embedded allowed database programs" and proves that embedded allowed stratified programs satisfying certain constraints are embedded domain independent. It also develops an algorithm for translating embedded allowed queries into equivalent algebraic expressions as a basis for evaluating safe queries in all calculus-based query classes. The second part of this thesis considers the issue of query optimisation for nested relational databases. Within a restricted set of nested schema trees, a join operator, called P-join, is proposed. The P-join operator does not require as many restructuring operators and combines the advantages of the extended natural join and recursive join for efficient data access. A P-join algorithm which takes advantage of a decomposed storage model and various join techniques available in the standard relational model to reduce the cost of join operation in nested relational databases is also proposed. Finally, this thesis investigates some algebraic properties of nested relational operators which are useful for query optimisation in the nested relational model and outlines a heuristic optimisation algorithm for nested relational expressions by adopting algebraic transformation rules developed in this thesis and previous related work