The complexity of querying indefinite information: defined relations, recursion and linear order

Abstract

This dissertation studies the computational complexity of answering queries in logical databases containing indefinite information arising from two sources: facts stated in terms of defined relations, and incomplete information about linearly ordered domains. First, we consider databases consisting of (1) a DATALOG program and (2) a description of the world in terms of the predicates defined by the program as well as the basic predicates. The query processing problem in such databases is related to issues in database theory, including view updates and DATALOG optimization, and also to the Artificial Intelligence problems of reasoning in circumscribed theories and sceptical abductive reasoning. If the program is non-recursive, the meaning of the database can be represented by Clark's Predicate Completion,...