# Model Theoretic Characterisations of Description Logics

arXiv: https://arxiv.org/abs/1305.5820 · HTML: https://mlsanity.com/paper/1305.5820/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 May 2013.

## Built on by (most cited first, 2 of 2)

- [Lutz's Spoiler Technique Revisited: A Unified Approach to Worst-Case Optimal Entailment of Unions of Conjunctive Queries in Locally-Forward Description Logics](https://mlsanity.com/paper/2108.05680/) (2021)
- [Fitting Horn DL Ontologies to ABox and Query Examples: A Tale of Simulation Quantifiers and Finite Models](https://mlsanity.com/paper/2604.26976/) (2026)

## Abstract (arXiv)

This thesis studies the model theoretic properties of the Description Logics (DLs) ALC, ALCI, ALCQ, as well as ALCO, ALCQO, ALCQIO and EL. TBoxes of ALC, ALCI and ALCQ are characterised as fragments of FO which are invariant under global bisimulation and disjoint unions. The logics ALCO, ALCQO and ALCQIO, which incorporate individuals, are characterised w.r.t. to the class K of all interpretations which interpret individuals as singleton sets. The characterisations for TBoxes of ALCO and ALCQO both require additionally that an FO-sentence is, under certain circumstances, preserved under forward generated subinterpretations. FO-sentences equivalent to ALCQIO-TBoxes, are - due to ALCQIO's inverse roles - characterised similarly but are required to be preserved under generated subinterpretations. EL as sub-boolean DL is characterised on concept level as the FO-fragment which is preserved under simulation and preserved under direct products. Equally valid is the characterisation by being preserved under simulation and having minimal models. For EL-TBoxes, a global version of simulation was not sufficient but FO-sentences of EL-TBoxes are invariant under global equi-simulation, disjoint unions and direct products. For each of these description logics, the characteristic concepts are explicated and the characterisation is accompanied by an investigation under which notion of saturation the logic in hand enjoys the Hennessy-and-Milner-Property. As application of the results we determine the minimal globally bisimilar companion w.r.t. ALCQO-bisimulation and introduce the L1-to-L2-rewritability problem for TBoxes, where L1 and L2 are (description) logics. The latter is the problem to decide whether or not an L1-TBox can be equivalently expressed as L2-TBox. We give algorithms which decide ALCI-to-ALC-rewritability and ALC-to-EL-rewritability. (See also abstract in the thesis.)