@article{Artale_Jung_Mazzullo_Ozaki_Wolter_2021, title={Living Without Beth and Craig: Definitions and Interpolants in Description Logics with Nominals and Role Inclusions}, volume={35}, url={https://ojs.aaai.org/index.php/AAAI/article/view/16770}, DOI={10.1609/aaai.v35i7.16770}, abstractNote={The Craig interpolation property (CIP) states that an interpolant for an implication exists iff it is valid. The projective Beth definability property (PBDP) states that an explicit definition exists iff a formula stating implicit definability is valid. Thus, the CIP and PBDP transform potentially hard existence problems into deduction problems in the underlying logic. Description Logics with nominals and/or role inclusions do not enjoy the CIP nor PBDP, but interpolants and explicit definitions have many potential applications in ontology engineering and ontology-based data management. In this article we show the following: even without Craig and Beth, the existence of interpolants and explicit definitions is decidable in description logics with nominals and/or role inclusions such as ALCO, ALCH and ALCHIO. However, living without Craig and Beth makes this problem harder than deduction: we prove that the existence problems become 2EXPTIME-complete, thus one exponential harder than validity. The existence of explicit definitions is 2EXPTIME-hard even if one asks for a definition of a nominal using any symbol distinct from that nominal, but it becomes EXPTIME-complete if one asks for a definition of a concept name using any symbol distinct from that concept name.}, number={7}, journal={Proceedings of the AAAI Conference on Artificial Intelligence}, author={Artale, Alessandro and Jung, Jean Christoph and Mazzullo, Andrea and Ozaki, Ana and Wolter, Frank}, year={2021}, month={May}, pages={6193-6201} }