First-order logic and automated theorem proving (2nd ed.)
First-order logic and automated theorem proving (2nd ed.)
Eliminating definitions and Skolem functions in first-order logic
ACM Transactions on Computational Logic (TOCL)
Reasoning in expressive description logics
Handbook of automated reasoning
The description logic handbook: theory, implementation, and applications
The description logic handbook: theory, implementation, and applications
Interpolation and Definability in Modal Logics (Oxford Logic Guides)
Interpolation and Definability in Modal Logics (Oxford Logic Guides)
Complexity and succinctness of public announcement logic
AAMAS '06 Proceedings of the fifth international joint conference on Autonomous agents and multiagent systems
Artificial Intelligence
Keys, nominals, and concrete domains
Journal of Artificial Intelligence Research
Effective query rewriting with ontologies over DBoxes
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
Views and queries: Determinacy and rewriting
ACM Transactions on Database Systems (TODS)
Beth definability in expressive description logics
Journal of Artificial Intelligence Research
Exact query reformulation over databases with first-order and description logics ontologies
Journal of Artificial Intelligence Research
Hi-index | 0.00 |
The Beth definability property, a well-known property from classical logic, is investigated in the context of description logics (DLs): if a general LTBox implicitly defines an L-concept in terms of a given signature, where L is a DL, then does there always exist over this signature an explicit definition in L for the concept? This property has been studied before and used to optimize reasoning in DLs. In this paper a complete classification of Beth definability is provided for extensions of the basic DL ALC with transitive roles, inverse roles, role hierarchies, and/or functionality restrictions, both on arbitrary and on finite structures. Moreover, we present a tableau-based algorithm which computes explicit definitions of at most double exponential size. This algorithm is optimal because it is also shown that the smallest explicit definition of an implicitly defined concept may be double exponentially long in the size of the input TBox. Finally, if explicit definitions are allowed to be expressed in first-order logic then we show how to compute them in EXPTIME.