A Van Benthem Theorem for Horn Description and Modal Logic

We introduce Horn simulations between interpretations and show that a first-order formula is equivalent to a Horn-ALC concept iff it is preserved under Horn simulations. Preservation under global Horn simulations characterizes first-order sentences equivalent to Horn-ALC TBoxes. We use Horn simulations to show that not every ALC concept (TBox) equivalent to a Horn FO formula is equivalent to a Horn-ALC concept (respectively TBox). For Horn modal logic, we thus solve an open problem posed by Sturm.

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