  In this paper we address the problem of handling inconsistencies in tables
with missing values (also called nulls) and functional dependencies. Although
the traditional view is that table instances must respect all functional
dependencies imposed on them, it is nevertheless relevant to develop theories
about how to handle instances that violate some dependencies. Regarding missing
values, we make no assumptions on their existence: a missing value exists only
if it is inferred from the functional dependencies of the table.
  We propose a formal framework in which each tuple of a table is associated
with a truth value among the following: true, false, inconsistent or unknown;
and we show that our framework can be used to study important problems such as
consistent query answering, table merging, and data quality measures - to
mention just a few. In this paper, however, we focus mainly on consistent query
answering, a problem that has received considerable attention during the last
decades.
  The main contributions of the paper are the following: (a) we introduce a new
approach to handle inconsistencies in a table with nulls and functional
dependencies, (b) we give algorithms for computing all true, inconsistent and
false tuples, (c) we investigate the relationship between our approach and
Four-valued logic in the context of data merging, and (d) we give a novel
solution to the consistent query answering problem and compare our solution to
that of table repairs.
