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Computational Complexity of Semantic Web Language

Computational Complexity of Semantic Web Language. Computational Properties. When evaluating the complexity, the following parameters will be considered: The Data Complexity : the complexity measured with respect to the number of facts in the ontology.

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Computational Complexity of Semantic Web Language

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  1. Computational Complexity of Semantic Web Language

  2. Computational Properties When evaluating the complexity, the following parameters will be considered: • The Data Complexity: the complexity measured with respect to the number of facts in the ontology. • The Taxonomic complexity: the complexity measured with respect to the size of the axioms in the ontology. • The Query Complexity: the complexity measured with respect to the number of conjuncts in the conjunctive query. • The Combined Complexity: the complexity measured with respect to both the size of the axioms and the number of facts. In the case of conjunctive query answering, the combined complexity also includes the query complexity.

  3. The reasoning problems considered here are the following: • Ontology Consistency: Check whether a given ontology has at least one model. • Concept Satisfiability: Given an ontology O and a class A, verify whether there is a model of O in which the interpretation of A is a non-empty set. • Concept Subsumption: Given an ontology O and two classes A, B, verify whether the interpretation of A is a subset of the interpretation of B in every model of O • Instance Checking: Given an ontology, an individual a and a class A, verify whether a is an instance of A in every model of the ontology. • Conjunctive Query Answering: Given an ontology O and a conjunctive query q, return the answers of the query with respect to O.

  4. Whenever the complexity for a given problem is described as Open, with a star, (*), it is meant that its decidability is still an open question; if the star (*) is omitted, then the problem is known to be decidable but precise complexity bounds have not yet been established. If a problem is labeled as trivial, it is meant that the language is not expressive enough for allowing to different possible answers to the problem, e.g. every RDF Schema ontology is known to be consistent.

  5. The fact that data complexity stays LOGSPACE, means that one can exploit relational database technology for instance checking and conjunctive query answering. The fact that data complexity goes beyond LOGSPACE means that query answering and instance checking require more powerful engines than the ones provided by relational database technologies. PTIME-hardness essentially requires Datalog technologies. For the CoNP cases, Disjunctive Datalog technologies could be adopted.

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