Living Without Beth and Craig: Definitions and Interpolants in Description Logics with Nominals and Role Inclusions
| Autor: | Alessandro Artale, Jean Christoph Jung, Andrea Mazzullo, Ana Ozaki, Frank Wolter |
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| Rok vydání: | 2021 |
| Předmět: | |
| Zdroj: | Proceedings of the AAAI Conference on Artificial Intelligence. 35:6193-6201 |
| ISSN: | 2374-3468 2159-5399 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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