  The query containment problem is a fundamental algorithmic problem in data
management. While this problem is well understood under set semantics, it is by
far less understood under bag semantics. In particular, it is a long-standing
open question whether or not the conjunctive query containment problem under
bag semantics is decidable. We unveil tight connections between information
theory and the conjunctive query containment under bag semantics. These
connections are established using information inequalities, which are
considered to be the laws of information theory. Our first main result asserts
that deciding the validity of maxima of information inequalities is many-one
equivalent to the restricted case of conjunctive query containment in which the
containing query is acyclic; thus, either both these problems are decidable or
both are undecidable. Our second main result identifies a new decidable case of
the conjunctive query containment problem under bag semantics. Specifically, we
give an exponential time algorithm for conjunctive query containment under bag
semantics, provided the containing query is chordal and admits a simple
junction tree.
