Pascal Hitzler

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Exercise 8.1. Transform the following concepts into negation normal form: (a) ¬(A u ∀r.B) (b) ¬∀r.∃s.(¬B t ∃r.A) (c) ¬((¬A u ∃r.>) t> 3 s.(A t ¬B)) Exercise 8.2. Apply the tableau algorithm in order to check if the axiom A v B is a logical consequence of the TBox {¬C v B,A u C v ⊥}. Exercise 8.3. Aply the tableau algorithm in order to check satisfiability(More)
With the advent of the Semantic Web, description logics have become one of the most prominent paradigms for knowledge representation and reasoning. Progress in research and applications, however, is constrained by the lack of well-structured knowledge bases consisting of a sophisticated schema and instance data adhering to this schema. It is paramount that(More)
We introduce ELP as a decidable fragment of the Semantic Web Rule Language (SWRL) that admits reasoning in polynomial time. ELP is based on the tractable description logic EL, and encompasses an extended notion of the recently proposed DL rules for that logic. Thus ELP extends EL with a number of features introduced by the forthcoming OWL 2, such as(More)
With the advent of the Semantic Web, description logics have become one of the most prominent paradigms for knowledge representation and reasoning. Progress in research and applications, however, faces a bottleneck due to the lack of available knowledge bases, and it is paramount that suitable automated methods for their acquisition will be developed. In(More)
Description logics (DLs) have become a prominent paradigm for representing knowledge in a variety of application areas, partly due to their ability to achieve a favourable balance between expressivity of the logic and performance of reasoning. Horn description logics are obtained, roughly speaking, by disallowing all forms of disjunctions. They have(More)
The Web Ontology Language OWL is currently the most prominent formalism for representing ontologies in Semantic Web applications. OWL is based on description logics, and automated reasoners are used to infer knowledge implicitly present in OWL ontologies. However, because typical description logics obey the classical principle of explosion, reasoning over(More)
An ontology alignment is the expression of relations between different ontologies. In order to view alignments independently from the language expressing ontologies and from the techniques used for finding the alignments, we use a category-theoretical model in which ontologies are the objects. We introduce a categorical structure, called V-alignment, made(More)
The Web of Data currently coming into existence through the Linked Open Data (LOD) effort is a major milestone in realizing the Semantic Web vision. However, the development of applications based on LOD faces difficulties due to the fact that the different LOD datasets are rather loosely connected pieces of information. In particular, links between LOD(More)
We introduce description logic (DL) rules as a new rule-based formalism for knowledge representation in DLs. As a fragment of the Semantic Web Rule Language SWRL, DL rules allow for a tight integration with DL knowledge bases. In contrast to SWRL, however, the combination of DL rules with expressive description logics remains decidable, and we show that the(More)