Efficient methods of processing unanticipated queries are a crucial prerequisite for the success of generalized database management systems. A wide variety of approaches to improve the performance of query evaluation algorithms have been proposed: logic-based and semantic transformations, fast implementations of basic operations, and combinatorial or heuristic algorithms for generating alternative access plans and choosing among them. These methods are presented in the framework of a general query evaluation procedure using the relational calculus representation of queries. In addition, nonstandard query optimization issues such as higher level query evaluation, query optimization in distributed databases, and use of database machines are addressed. The focus, however, is on query optimization in centralized database systems.

We present an extension of Horn-clause logic which can hypothetically add and delete tuples from a database. Such logics have been discussed in the literature, but their complexities and expressibilities have remained an open question. This paper examines two such logics in the function-free, predicate case. It is shown, in particular, that augmenting Horn-clause logic with hypothetical addition increases its data-complexity from PTIME to PSPACE. When deletions are added as well, complexity increases again, to EXPTIME. We then augment the logic with negation-as-failure and develop the notion of stratified hypothetical rulebases. It is shown that negation does not increase complexity. To establish expressibility, we view the logic as a query language for relational databases. It is shown that any typed generic query that is computable in PSPACE can be expressed as a stratified rulebase of hypothetical additions. Similarly, any typed generic query that is computable in EXPTIME can be exp...

In this paper we characterise exactly the complexity of a set based database language called SRL, which presents a unified framework for queries and updates. By imposing simple syntactic restrictions on it, we are able to express exactly the classes, P and LOGSPACE. We also discuss the role of ordering in database query languages and show that the hom operator of Machiavelli language in [OBB89] does not capture all the order-independent properties.

Abstract. Open answer set programming (OASP) is an extension of answer set programming where one may ground a program with an arbitrary superset of the program’s constants. We define a fixed point logic (FPL) extension of Clark’s completion such that open answer sets correspond to models of FPL formulas and identify a syntactic subclass of programs, called (loosely) guarded programs. Whereas reasoning with general programs in OASP is undecidable, the FPL translation of (loosely) guarded programs falls in the decidable (loosely) guarded fixed point logic (µ(L)GF). Moreover, we reduce normal closed ASP to loosely guarded OASP, enabling a characterization of an answer set semantics by µLGF formulas. Finally, we relate guarded OASP to Datalog LITE, thus linking an answer set semantics to a semantics based on fixed point models of extended stratified Datalog programs. From this correspondence, we deduce 2-EXPTIME-completeness of satisfiability checking w.r.t. (loosely) guarded programs. 1

Abstract. We extend the open answer set semantics for programs with generalized literals. Such extended programs (EPs) have interesting properties, e.g. the ability to express infinity axioms- EPs that have but infinite answer sets. However, reasoning under the open answer set semantics, in particular satisfiability checking of a predicate w.r.t. a program, is already undecidable for programs without generalized literals. In order to regain decidability, we restrict the syntax of EPs such that both rules and generalized literals are guarded. Viaa translation to guarded fixed point logic (µGF), in which satisfiability checking is 2-EXPTIME-complete, we deduce 2-EXPTIME-completeness of satisfiability checking in such guarded EPs (GEPs). Bound GEPs are restricted GEPs with EXPTIME-complete satisfiability checking, but still sufficiently expressive to optimally simulate computation tree logic (CTL). We translate Datalog LITE programs to GEPs, establishing equivalence of GEPs under an open answer set semantics, alternation-free µGF, and Datalog LITE. Finally, we discuss ω-restricted logic programs under an open answer set semantics. 1

We propose a language which can express every computable query. The language is syntactically based on the first-order predicate calculus, but semantically is interpreted as post-conditions, unlike the customary calculus query languages. The language has a capability to restrict itself to reasonable queries, accepting criteria of reasonability as a parameter.

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