Computational Complexity of

farmpaintlickInternet and Web Development

Oct 21, 2013 (3 years and 9 months ago)

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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.


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.


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.



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.


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.