  We investigate the combination of fragments of classical logic as a way of
conservatively extending a given Boolean logic by the addition of new
connectives, and we precisely characterize the circumstances in which such a
combination produces the corresponding fragment of classical logic over the
signature containing connectives from both fragments given as input. If the
thereby produced combined fragment is only incompletely characterized by the
components given as input, this means that connectives from one component need
to interact with connectives from the other component, giving rise to
interaction principles. The main contributions strongly rely on the
(well-known) description of the 2-valued clones made by Post, on the (not so
well-known) axiomatization procedures for 2-valued matrices laid out by
Rautenberg, and on Avron's non-deterministic matrices, which have (recently)
been used to produce a significant advance on the understanding of the
semantics of fibring.
