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First-order logic and automated theorem proving (2nd ed.)
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TABLEAUX '98 Proceedings of the International Conference on Automated Reasoning with Analytic Tableaux and Related Methods
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ACM Transactions on Computational Logic (TOCL)
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Handbook of automated reasoning
The description logic handbook
The description logic handbook
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The description logic handbook
The description logic handbook
Elements Of Finite Model Theory (Texts in Theoretical Computer Science. An Eatcs Series)
Elements Of Finite Model Theory (Texts in Theoretical Computer Science. An Eatcs Series)
Interpolation and Definability in Modal Logics (Oxford Logic Guides)
Interpolation and Definability in Modal Logics (Oxford Logic Guides)
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AAMAS '06 Proceedings of the fifth international joint conference on Autonomous agents and multiagent systems
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Journal of Automated Reasoning
Artificial Intelligence
TABLEAUX '07 Proceedings of the 16th international conference on Automated Reasoning with Analytic Tableaux and Related Methods
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Journal of Artificial Intelligence Research
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IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
Effective query rewriting with ontologies over DBoxes
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
The complexity of finite model reasoning in description logics
Information and Computation - Special issue: 19th international conference on automated deduction (CADE-19)
Views and queries: Determinacy and rewriting
ACM Transactions on Database Systems (TODS)
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Proceedings of the 2010 conference on ECAI 2010: 19th European Conference on Artificial Intelligence
Determinacy and query rewriting for conjunctive queries and views
Theoretical Computer Science
Conjunctive queries determinacy and rewriting
Proceedings of the 14th International Conference on Database Theory
Foundations for uniform interpolation and forgetting in expressive description logics
IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume Two
Beth definability in expressive description logics
IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume Two
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The Beth definability property, a well-known property from classical logic, is investigated in the context of description logics: if a general L-TBox implicitly defines an L-concept in terms of a given signature, where L is a description logic, 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 description logics. In this paper a complete classification of Beth definability is provided for extensions of the basic description logic 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 single exponential time.