Model Comparison Games for Horn Description Logics
2019 34th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)
Horn description logics are syntactically defined fragments of standard description logics that fall within the Horn fragment of first-order logic and for which ontologymediated 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
... hem to obtain an Ehrenfeucht-Fraïssé 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-Fraïssé 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. 1 The results obtained in this paper could have been presented as a contribution to modal rather than description logic. The only reason why we have chosen the DL environment is that the impact of Horn fragments in description logic has so far been much more significant than in modal logic.