  Modal logic is a paradigm for several useful and applicable formal systems in
computer science. It generally retains the low complexity of classical
propositional logic, but notable exceptions exist in the domains of
description, temporal, and spatial logic, where the most expressive formalisms
have a very high complexity or are even undecidable. In search of
computationally well-behaved fragments, clausal forms and other
sub-propositional restrictions of temporal and description logics have been
recently studied. This renewed interest on sub-propositional logics, which
mainly focus on the complexity of the various fragments, raise natural
questions on their the relative expressive power, which we try to answer here
for the basic multi-modal logic Kn. We consider the Horn and the Krom
restrictions, as well as the combined restriction (known as the core fragment)
of modal logic, and, orthogonally, the fragments that emerge by disallowing
boxes or diamonds from positive literals. We study the problem in a very
general setting, to ease transferring our results to other meaningful cases.
