On the representation and querying of sets of possible worlds

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We represent a set of possible worlds using an incomplete information database. The representation techniques that we study range from the very simple Codd-table (a relation over constants and uniquely occurring variables called nulls) to much more complex mechanisms involving views of conditioned-tables (programs applied to Codd-tables augmented by equality and inequality conditions). (1) We provide matching upper and lower bounds on the data-complexity of testing containment, membership and uniqueness for sets of possible worlds. We fully classify these problems with respect to our representations. (2) We investigate the data-complexity of querying incomplete information databases for both possible and certain facts. For each fixed positive existential query on conditioned-tables we present a polynomial time algorithm solving the possible fact problem. We match this upper bound by two NP-completeness lower bounds, when the fixed query contains either negation or recursion and is applied to Codd-tables. Finally, we show that the certain fact problem is coNP-complete, even for a fixed first order query applied to a Codd-table.