  Datalog+/- is a Datalog-based language family enhanced with existential
quantification in rule heads, equalities and negative constraints. Query
answering over databases with respect to a Datalog+/- theory is generally
undecidable, however several syntactic restrictions have been proposed to
remedy this fact. However, a useful and natural feature however is as of yet
missing from Datalog+/-: The ability to express uncertain knowledge, or
choices, using disjunction. It is the precise objective of the doctoral thesis
herein discussed, to investigate the impact on the complexity of query
answering, of adding disjunction to well-known decidable Datalog+/- fragments,
namely guarded, sticky and weakly-acyclic Datalog+/- theories. For guarded
theories with disjunction, we obtain a strong 2EXP lower bound in the combined
complexity, even for very restricted formalisms like fixed sets of
(disjunctive) inclusion dependencies. For sticky theories, the query answering
problem becomes undecidable, even in the data complexity, and for
weakly-acyclic query answering we see a reasonable and expected increase in
complexity.
