Artificial Intelligence
Logic for problem-solving
An amateur's introduction to recursive query processing strategies
SIGMOD '86 Proceedings of the 1986 ACM SIGMOD international conference on Management of data
Clausal intuitionistic logic I. Fixed-point semantics
Journal of Logic Programming
Clausal intuitionistic logic II. Tableau proof procedures
Journal of Logic Programming
Hypothetical datalog: complexity and expressibility
Lecture notes in computer science on ICDT '88
Towards a theory of declarative knowledge
Foundations of deductive databases and logic programming
On the declarative semantics of deductive databases and logic programs
Foundations of deductive databases and logic programming
Hypothetical datalog: complexity and expressibility
Theoretical Computer Science
Introduction To Automata Theory, Languages, And Computation
Introduction To Automata Theory, Languages, And Computation
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
The complexity of relational query languages (Extended Abstract)
STOC '82 Proceedings of the fourteenth annual ACM symposium on Theory of computing
Relational queries computable in polynomial time (Extended Abstract)
STOC '82 Proceedings of the fourteenth annual ACM symposium on Theory of computing
A dynamic logic programming language for relational updates
A dynamic logic programming language for relational updates
On the complexity of propositional knowledge base revision, updates, and counterfactuals
PODS '92 Proceedings of the eleventh ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Deductive database languages: problems and solutions
ACM Computing Surveys (CSUR)
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This paper examines an extension of Horn logic in which rules can add entries to a database hypothetically. Several researchers have developed logical systems along these lines, but the complexity and expressibility of such logics is only now being explored. It has been shown, for instance, that the data-complexity of these logics is PSPACE-complete in the function-free, predicate case. This paper extends this line of research by developing syntactic restrictions with lower complexity. These restrictions are based on two ideas from Horn-clause logic: linear recursion and stratified negation. In particular, a notion of stratification is developed in which negation-as-failure alternates with linear recursion. The complexity of such rulebases depends on the number of layers of stratification. The result is a hierarchy of syntactic classes which corresponds exactly in the polynomial-time hierarchy of complexity classes. In particular, rulebases with k strata are data-complete for &Sgr;Ph. Furthermore, these rulebases provide a complete characterization of the relational queries in &Sgr;Ph. That is, any query whose graph is in &Sgr;Ph can be represented as a set of hypothetical rules with k strata. Unlike other expressibility results in the literature, this result does not require the data domain to be linearly ordered.