A Summary of the PhD Dissertation Methods for evaluating queries to Horn knowledge bases in first-order logic

Query languages and query processing are important topics in computer science and information technology, as they are widely used in practical applications. Query languages are usually designed so that intensional predicates can be defined by logic rules and query evaluation can be done in polynomial time in the size of the extensional relations. Studying query processing for a query language involves developing an evaluation method with a good data complexity for the language (e.g., with polynomial time data complexity if the language allows) and then developing various optimizations for the method. Datalog is a well-known rule language for deductive databases. It expresses a Horn fragment without function symbols of first-order logic. Programs in Datalog are required to be range-restricted in the sense that every variable occurring in the head of a program clause also occurs in the body of the clause. Datalog uses the traditional monotonic semantics. The extension Datalog¬ of Datalog allows negation in the bodies of program clauses and uses a non-monotonic semantics like the standard semantics for stratified Datalog¬ programs and the well-founded semantics for the general case. Interest in deductive databases and methods for evaluating Datalog or Datalog¬ queries intensified in the eighties and early nineties, but “a perceived lack of compelling applications at the time ultimately forced Datalog research into a long dormancy” [19]. As also observed by Huang et al. in their SIGMOD’2011 paper [19]: