  Horn description logics are syntactically defined fragments of standard
description logics that fall within the Horn fragment of first-order logic and
for which ontology-mediated query answering is in PTime for data complexity.
They were independently introduced in modal logic to capture the intersection
of Horn first-order logic with modal logic. In this paper, we introduce model
comparison games for the basic Horn description logic hornALC (corresponding to
the basic Horn modal logic) and use them to obtain an Ehrenfeucht-Fra\"iss\'e
type definability result and a van Benthem style expressive completeness result
for hornALC. We also establish a finite model theory version of the latter. The
Ehrenfeucht-Fra\"iss\'e type definability result is used to show that checking
hornALC indistinguishability of models is ExpTime-complete, which is in sharp
contrast to ALC indistinguishability (i.e., bisimulation equivalence) checkable
in PTime. In addition, we explore the behavior of Horn fragments of more
expressive description and modal logics by defining a Horn guarded fragment of
first-order logic and introducing model comparison games for it.
