A categorical approach to study model comparison games in terms of comonads was recently initiated by Abramsky et al. In this work, we analyse games that appear naturally in the context of description logics and supplement them with suitable game comonads. More precisely, we consider expressive sublogics of ALCSelfIbO, namely, the logics that extend ALC with any combination of inverses, nominals, safe boolean roles combinations, and Self operator. Our construction augments and modifies the so-called modal comonad by Abramsky and Shah. The approach that we took heavily relies on the use of relative comonads, which we leverage to encapsulate additional capabilities within the bisimulation games in a compositional manner.

翻译：最近,Abramsky等人发起了一种明确的方法,从共鸣的角度来研究模式比较游戏。在这项工作中,我们分析了在描述逻辑方面自然出现的游戏,并以合适的共鸣来补充这些游戏。更准确地说,我们考虑了ALCFIbO的表达亚逻辑,即将ALC延伸至反向、名义、安全的布尔恩角色组合和自我操作者组合的任何组合的逻辑。我们的建筑扩大并修改了Abramsky和Shah的所谓模式共鸣。我们采取的方法在很大程度上依赖于使用相对的共鸣,我们利用这些相对的共鸣,以组合的方式将更多的能力包罗在刺激游戏中。