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

Model Comparison Games for Horn Description Logics