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...d reasoning, and it is often used to guide the design of ontology languages. A good textbook introduction to the field is provided by Sipser [41], a more extensive treatment is given by Papadimitriou =-=[35]-=-. Alternating Turing Machines were originally introduced in [9]. The proof of ExpTime-hardness for reasoning in combinations of OWL profiles that is given in Section 4.5 has first been formulated in [...

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...n works on data quality and cleaning in the context of reasoning, where noisy data can have stronger effects [15]. OWL QL was originally inspired by the so-called DL-Lite family of description logics =-=[8]-=-. The current W3C standard is closely related to the logic DL-LiteR, later called DL-LiteR core [1]. Query rewriting can often lead to a huge number of ABox queries, and various suggestions have been ...

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... information on OWL EL and its implementation can be found in a number of research papers. Basic investigations on the related description logic EL ++ have first been made by Baader, Brandt, and Lutz =-=[3]-=-, who also introduced the extension with property ranges that is used in OWL EL [4]. Implementation aspects have been180 M. Krötzsch discussed in detail in a series of recent works related to the OWL...

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...in previous lecture notes of the Reasoning Web Summer School: Rudolph provides a detailed discussion of DL semantics and modelling [38], Baader gives a general overview with extended historical notes =-=[2]-=-, and Sattler focusses on tableau-based reasoning methods [39]. An introduction to conjunctive query answering in description logics is given by Ortiz and Simkus in another chapter of these lecture no...

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...r when OWL QL has been designed: the slightest change of expressivity can lead to different computational properties, and there are a great number of feature combinations. A good overview is given in =-=[1]-=-, where the authors study 40 different logics. In their terminology, our QL normal form is closely related to the logic DL-Lite H horn whereas the OWL QL is based on DL-LiteH core . QL normal form is ...

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... under additional restrictions [26]. Efficient solutions were proposed for sublanguages of OWL EL [30,24]. OWL RL is often studied as an extension of the Semantic Web data representation standard RDF =-=[22]-=- with additional inference rules. Relevant sublanguages that cover only some features of OWL RL include RDF Schema [7] and pD∗ (a.k.a. OWL-Horst) [17]. The OWL standard includes a set of inference rul...

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...the Semantic Web data representation standard RDF [22] with additional inference rules. Relevant sublanguages that cover only some features of OWL RL include RDF Schema [7] and pD∗ (a.k.a. OWL-Horst) =-=[17]-=-. The OWL standard includes a set of inference rules that are formulated in terms of the RDF encoding of OWL [32]. In contrast to OWL EL, the main focus of many OWL RL implementations is on large data...

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...papers. Basic investigations on the related description logic EL ++ have first been made by Baader, Brandt, and Lutz [3], who also introduced the extension with property ranges that is used in OWL EL =-=[4]-=-. Implementation aspects have been180 M. Krötzsch discussed in detail in a series of recent works related to the OWL EL reasoner ELK [18,19,21]. A discussion of the engineering aspects of implementin...

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...EL reasoner ELK [18,19,21]. A discussion of the engineering aspects of implementing such a saturationbased system can be found in a technical report [20]. Other dedicated OWL EL reasoners include CEL =-=[6]-=-, Snorocket [29], and jCEL [31]. The general-purpose OWL reasoner Pellet uses special algorithms if the input ontology belongs to a certain subset of OWL EL, allowing it to classify some large OWL EL ...

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...nctive query answering in OWL EL tends to be harder than in OWL QL and OWL RL, and is intractable even under additional restrictions [26]. Efficient solutions were proposed for sublanguages of OWL EL =-=[30,24]-=-. OWL RL is often studied as an extension of the Semantic Web data representation standard RDF [22] with additional inference rules. Relevant sublanguages that cover only some features of OWL RL inclu...

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...in OWL RL, since the saturated ontology can simply be queried like an extended database. Academic research in OWL RL has strongly focussed on aspects of scalability and distribution; examples include =-=[43,16,25,15,44,42]-=-. There have also been works on data quality and cleaning in the context of reasoning, where noisy data can have stronger effects [15]. OWL QL was originally inspired by the so-called DL-Lite family o...

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...uced the extension with property ranges that is used in OWL EL [4]. Implementation aspects have been180 M. Krötzsch discussed in detail in a series of recent works related to the OWL EL reasoner ELK =-=[18,19,21]-=-. A discussion of the engineering aspects of implementing such a saturationbased system can be found in a technical report [20]. Other dedicated OWL EL reasoners include CEL [6], Snorocket [29], and j...

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...ndard is closely related to the logic DL-LiteR, later called DL-LiteR core [1]. Query rewriting can often lead to a huge number of ABox queries, and various suggestions have been made to improve this =-=[24,12,23,37]-=-. The only freely available implementation for OWL QL appears to be Owlgres. 13 Another implementation, QuOnto, 14 is available to registered users. Some query rewriting approaches in OWL RL systems c...

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...ndard is closely related to the logic DL-LiteR, later called DL-LiteR core [1]. Query rewriting can often lead to a huge number of ABox queries, and various suggestions have been made to improve this =-=[24,12,23,37]-=-. The only freely available implementation for OWL QL appears to be Owlgres. 13 Another implementation, QuOnto, 14 is available to registered users. Some query rewriting approaches in OWL RL systems c...

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...in OWL RL, since the saturated ontology can simply be queried like an extended database. Academic research in OWL RL has strongly focussed on aspects of scalability and distribution; examples include =-=[43,16,25,15,44,42]-=-. There have also been works on data quality and cleaning in the context of reasoning, where noisy data can have stronger effects [15]. OWL QL was originally inspired by the so-called DL-Lite family o...

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...nctive query answering in OWL EL tends to be harder than in OWL QL and OWL RL, and is intractable even under additional restrictions [26]. Efficient solutions were proposed for sublanguages of OWL EL =-=[30,24]-=-. OWL RL is often studied as an extension of the Semantic Web data representation standard RDF [22] with additional inference rules. Relevant sublanguages that cover only some features of OWL RL inclu...

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...in OWL RL, since the saturated ontology can simply be queried like an extended database. Academic research in OWL RL has strongly focussed on aspects of scalability and distribution; examples include =-=[43,16,25,15,44,42]-=-. There have also been works on data quality and cleaning in the context of reasoning, where noisy data can have stronger effects [15]. OWL QL was originally inspired by the so-called DL-Lite family o...

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...in OWL RL, since the saturated ontology can simply be queried like an extended database. Academic research in OWL RL has strongly focussed on aspects of scalability and distribution; examples include =-=[43,16,25,15,44,42]-=-. There have also been works on data quality and cleaning in the context of reasoning, where noisy data can have stronger effects [15]. OWL QL was originally inspired by the so-called DL-Lite family o...

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...arge OWL EL ontologies that would otherwise not be supported. Conjunctive query answering in OWL EL tends to be harder than in OWL QL and OWL RL, and is intractable even under additional restrictions =-=[26]-=-. Efficient solutions were proposed for sublanguages of OWL EL [30,24]. OWL RL is often studied as an extension of the Semantic Web data representation standard RDF [22] with additional inference rule...

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...in OWL RL, since the saturated ontology can simply be queried like an extended database. Academic research in OWL RL has strongly focussed on aspects of scalability and distribution; examples include =-=[43,16,25,15,44,42]-=-. There have also been works on data quality and cleaning in the context of reasoning, where noisy data can have stronger effects [15]. OWL QL was originally inspired by the so-called DL-Lite family o...

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...ndard is closely related to the logic DL-LiteR, later called DL-LiteR core [1]. Query rewriting can often lead to a huge number of ABox queries, and various suggestions have been made to improve this =-=[24,12,23,37]-=-. The only freely available implementation for OWL QL appears to be Owlgres. 13 Another implementation, QuOnto, 14 is available to registered users. Some query rewriting approaches in OWL RL systems c...

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...in OWL RL, since the saturated ontology can simply be queried like an extended database. Academic research in OWL RL has strongly focussed on aspects of scalability and distribution; examples include =-=[43,16,25,15,44,42]-=-. There have also been works on data quality and cleaning in the context of reasoning, where noisy data can have stronger effects [15]. OWL QL was originally inspired by the so-called DL-Lite family o...

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...ten studied as an extension of the Semantic Web data representation standard RDF [22] with additional inference rules. Relevant sublanguages that cover only some features of OWL RL include RDF Schema =-=[7]-=- and pD∗ (a.k.a. OWL-Horst) [17]. The OWL standard includes a set of inference rules that are formulated in terms of the RDF encoding of OWL [32]. In contrast to OWL EL, the main focus of many OWL RL ...

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...]. Alternating Turing Machines were originally introduced in [9]. The proof of ExpTime-hardness for reasoning in combinations of OWL profiles that is given in Section 4.5 has first been formulated in =-=[27]-=-, where additional related results can be found. In particular, it is shown there that the extension of OWL QL with universal quantifiers on the right, but without allowing general existential quantif...

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...+ i (35) FelisCatus ⊑ Animal T⊑ : (34), (33) (36) FelisCatus ⊑∃preysOn.Animal ⊓ Small T⊑ : (34), (31) (37) Animal ⊓ Small ⊑ Animal ⊓ Small T + i Animal ⊓ Small ⊑⊤ T + i Animal ⊓ Small ⊑ Animal : (38) =-=(40)-=- Animal ⊓ Small ⊑ Small T − : (38) ⊓ (41) FelisCatus ⊑∃preysOn.Animal T + : (37), (40) ∃ (42) FelisCatus ⊑ Animal ⊓∃preysOn.Animal T + : (36), (42) ⊓ (43) FelisCatus ⊑ Predator T⊑ : (43), (32) (44) We...

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... [18,19,21]. A discussion of the engineering aspects of implementing such a saturationbased system can be found in a technical report [20]. Other dedicated OWL EL reasoners include CEL [6], Snorocket =-=[29]-=-, and jCEL [31]. The general-purpose OWL reasoner Pellet uses special algorithms if the input ontology belongs to a certain subset of OWL EL, allowing it to classify some large OWL EL ontologies that ...

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...y languages. A good textbook introduction to the field is provided by Sipser [41], a more extensive treatment is given by Papadimitriou [35]. Alternating Turing Machines were originally introduced in =-=[9]-=-. The proof of ExpTime-hardness for reasoning in combinations of OWL profiles that is given in Section 4.5 has first been formulated in [27], where additional related results can be found. In particul...

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...ase of OWL QL, one should also define the meaning of conjunctive query answering under RDF-Based Semantics first, which is closely related to the semantics of SPARQL queries under RDF-Based Semantics =-=[10]-=-. This is also part of the upcoming W3C SPARQL 1.1 entailment regime for OWL RDF-Based Semantics [11]. Acknowledgements. The author would like to thank Yavor Nenov and an anonymous reviewer for their ...

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...uced the extension with property ranges that is used in OWL EL [4]. Implementation aspects have been180 M. Krötzsch discussed in detail in a series of recent works related to the OWL EL reasoner ELK =-=[18,19,21]-=-. A discussion of the engineering aspects of implementing such a saturationbased system can be found in a technical report [20]. Other dedicated OWL EL reasoners include CEL [6], Snorocket [29], and j...

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...uced the extension with property ranges that is used in OWL EL [4]. Implementation aspects have been180 M. Krötzsch discussed in detail in a series of recent works related to the OWL EL reasoner ELK =-=[18,19,21]-=-. A discussion of the engineering aspects of implementing such a saturationbased system can be found in a technical report [20]. Other dedicated OWL EL reasoners include CEL [6], Snorocket [29], and j...

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...discussion of the engineering aspects of implementing such a saturationbased system can be found in a technical report [20]. Other dedicated OWL EL reasoners include CEL [6], Snorocket [29], and jCEL =-=[31]-=-. The general-purpose OWL reasoner Pellet uses special algorithms if the input ontology belongs to a certain subset of OWL EL, allowing it to classify some large OWL EL ontologies that would otherwise...

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...comprehensive treatment of OWL, RDF, and related technologies, we recommend an introductory textbook [14]. For more information on description logics, the DL Primer provides a gentle first exposition =-=[28]-=-. More detailed introductions can be found in previous lecture notes of the Reasoning Web Summer School: Rudolph provides a detailed discussion of DL semantics and modelling [38], Baader gives a gener...

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...n(x, y) ∧ Animal(y) (52) 7 For a more detailed (and more formal) introduction to conjunctive queries in DLs, see the chapter Reasoning and Query Answering in Description Logics in these lecture notes =-=[33]-=-. 8 We will always use x, y, z for variables, so that no confusion with individual names is likely.152 M. Krötzsch specifies a query for all cats x that prey on some animal. The animal y is not part ...

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...ntle first exposition [28]. More detailed introductions can be found in previous lecture notes of the Reasoning Web Summer School: Rudolph provides a detailed discussion of DL semantics and modelling =-=[38]-=-, Baader gives a general overview with extended historical notes [2], and Sattler focusses on tableau-based reasoning methods [39]. An introduction to conjunctive query answering in description logics...

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...h is needed to show hardness of a computation task. We now recall the basic ideas and introduce some notation. Readers who are in need of a more thorough introduction should consult a textbook, e.g., =-=[41]-=-. The general vehicle to measure the hardness of a problem on computer science is the Turing machine. It provides us with a computational model: a standard platform on which we can “implement” algorit...

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...ail in a series of recent works related to the OWL EL reasoner ELK [18,19,21]. A discussion of the engineering aspects of implementing such a saturationbased system can be found in a technical report =-=[20]-=-. Other dedicated OWL EL reasoners include CEL [6], Snorocket [29], and jCEL [31]. The general-purpose OWL reasoner Pellet uses special algorithms if the input ontology belongs to a certain subset of ...

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... Rudolph provides a detailed discussion of DL semantics and modelling [38], Baader gives a general overview with extended historical notes [2], and Sattler focusses on tableau-based reasoning methods =-=[39]-=-. An introduction to conjunctive query answering in description logics is given by Ortiz and Simkus in another chapter of these lecture notes [33]. A basic reference for advanced topics in DL research...