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- Bernardo Cuenca Grau, Ian Horrocks, +4 authors Zhe Wang
- J. Artif. Intell. Res.
- 2013

Answering conjunctive queries (CQs) over a set of facts extended with existential rules is a prominent problem in knowledge representation and databases. This problem can be solved using the chase algorithm, which extends the given set of facts with fresh facts in order to satisfy the rules. If the chase terminates, then CQs can be evaluated directly in the… (More)

- Helle Hvid Hansen, Clemens Kupke
- Electr. Notes Theor. Comput. Sci.
- 2004

- Clemens Kupke, Alexander Kurz, Yde Venema
- Theor. Comput. Sci.
- 2003

In this paper we argue that the category of Stone spaces forms an interesting base category for coalgebras, in particular, if one considers the Vietoris functor as an analogue to the power set functor on the category of sets. We prove that the so-called descriptive general frames, which play a fundamental role in the semantics of modal logics, can be seen… (More)

- Corina Cîrstea, Clemens Kupke, Dirk Pattinson
- CSL
- 2009

The coalgebraic approach to modal logic provides a uniform framework that captures the semantics of a large class of structurally different modal logics, including e.g. graded and probabilistic modal logics and coalition logic. In this paper, we introduce the coalgebraic μ-calculus, an extension of the general (coalgebraic) framework with fixpoint… (More)

- Clemens Kupke, Alexander Kurz, Yde Venema
- Logical Methods in Computer Science
- 2012

We study the finitary version of the coalgebraic logic introduced by L. Moss. The syntax of this logic, which is introduced uniformly with respect to a coalgebraic type functor, required to preserve weak pullbacks, extends that of classical propositional logic with a so-called coalgebraic cover modality depending on the type functor. Its semantics is… (More)

- Clemens Kupke, Yde Venema
- 20th Annual IEEE Symposium on Logic in Computer…
- 2005

We generalize some of the central results in automata theory to the abstraction level of coalgebras. In particular, we show that for any standard, weak pullback preserving functor F, the class of recognizable languages of F -coalgebras is closed under taking unions, intersections and projections. Our main technical result concerns a construction which… (More)

- Georg Gottlob, André Hernich, Clemens Kupke, Thomas Lukasiewicz
- Description Logics
- 2012

We tackle the problem of defining a well-founded semantics for Datalog rules with existentially quantified variables in their heads and negations in their bodies. In particular, we provide a well-founded semantics (WFS) for the recent Datalog± family of ontology languages, which covers several important description logics (DLs). To do so, we generalize… (More)

We tackle a long-standing open research problem and prove the decidability of query answering under the stable model semantics for guarded existential rules, where rule bodies may contain negated atoms, and provide complexity results. The results extend to guarded Datalog± with negation, and thus provide a natural and decidable stable model semantics to… (More)

- Clemens Kupke, Alexander Kurz, Dirk Pattinson
- Electr. Notes Theor. Comput. Sci.
- 2004

With coalgebras usually being defined in terms of an endofunctor T on sets, this paper shows that modal logics for T -coalgebras can be naturally described as functors L on boolean algebras. Building on this idea, we study soundness, completeness and expressiveness of coalgebraic logics from the perspective of duality theory. That is, given a logic L for… (More)

- Bernardo Cuenca Grau, Ian Horrocks, +4 authors Zhe Wang
- KR
- 2012

Answering conjunctive queries (CQs) over a set of facts extended with existential rules is a key problem in knowledge representation and databases. This problem can be solved using the chase (aka materialisation) algorithm; however, CQ answering is undecidable for general existential rules, so the chase is not guaranteed to terminate. Several acyclicity… (More)