14,105 research outputs found
Practical Reasoning for Very Expressive Description Logics
Description Logics (DLs) are a family of knowledge representation formalisms
mainly characterised by constructors to build complex concepts and roles from
atomic ones. Expressive role constructors are important in many applications,
but can be computationally problematical. We present an algorithm that decides
satisfiability of the DL ALC extended with transitive and inverse roles and
functional restrictions with respect to general concept inclusion axioms and
role hierarchies; early experiments indicate that this algorithm is well-suited
for implementation. Additionally, we show that ALC extended with just
transitive and inverse roles is still in PSPACE. We investigate the limits of
decidability for this family of DLs, showing that relaxing the constraints
placed on the kinds of roles used in number restrictions leads to the
undecidability of all inference problems. Finally, we describe a number of
optimisation techniques that are crucial in obtaining implementations of the
decision procedures, which, despite the worst-case complexity of the problem,
exhibit good performance with real-life problems
On the Complexity and Expressiveness of Description Logics with Counting
Simple counting quantifiers that can be used to compare the number of role successors of an individual or the cardinality of a concept with a fixed natural number have been employed in Description Logics (DLs) for more than two decades under the respective names of number restrictions and cardinality restrictions on concepts. Recently, we have considerably extended the expressivity of such quantifiers by allowing to impose set and cardinality constraints formulated in the quantifier-free fragment of Boolean Algebra with Presburger Arithmetic (QFBAPA) on sets of role successors and concepts, respectively. We were able to prove that this extension does not increase the complexity of reasoning. In the present paper, we investigate the expressive power of the DLs obtained in this way, using appropriate bisimulation characterizations and 0–1 laws as tools to differentiate between the expressiveness of different logics. In particular, we show that, in contrast to most classical DLs, these logics are no longer expressible in first-order predicate logic (FOL), and we characterize their first-order fragments. In most of our previous work on DLs with QFBAPA-based set and cardinality constraints we have employed finiteness restrictions on interpretations to ensure that the obtained sets are finite, as required by the standard semantics for QFBAPA. Here we dispense with these restrictions to ease the comparison with classical DLs, where one usually considers arbitrary models rather than finite ones, easier. It turns out that doing so does not change the complexity of reasoning
Answering regular path queries mediated by unrestricted SQ ontologies
A prime application of description logics is ontology-mediated query answering, with the query language often reaching far beyond instance queries. Here, we investigate this task for positive existential two-way regular path queries and ontologies formulated in the expressive description logic , where denotes the extension of the basic description logic with transitive roles () and qualified number restrictions () which can be unrestrictedly applied to both non-transitive and transitive roles (). Notably, the latter is usually forbidden in expressive description logics. As the main contribution, we show decidability of ontology-mediated query answering in that setting and establish tight complexity bounds, namely 2ExpTime-completeness in combined complexity and coNP-completeness in data complexity. Since the lower bounds are inherited from the fragment , we concentrate on providing upper bounds. As main technical tools we establish a tree-like countermodel property and a characterization of when a query is not satisfied in a tree-like interpretation. Together, these results allow us to use an automata-based approach to query answering
On Bisimulations for Description Logics
We study bisimulations for useful description logics. The simplest among the
considered logics is (a variant of PDL). The others
extend that logic with inverse roles, nominals, quantified number restrictions,
the universal role, and/or the concept constructor for expressing the local
reflexivity of a role. They also allow role axioms. We give results about
invariance of concepts, TBoxes and ABoxes, preservation of RBoxes and knowledge
bases, and the Hennessy-Milner property w.r.t. bisimulations in the considered
description logics. Using the invariance results we compare the expressiveness
of the considered description logics w.r.t. concepts, TBoxes and ABoxes. Our
results about separating the expressiveness of description logics are naturally
extended to the case when instead of we have any sublogic
of that extends . We also provide results
on the largest auto-bisimulations and quotient interpretations w.r.t. such
equivalence relations. Such results are useful for minimizing interpretations
and concept learning in description logics. To deal with minimizing
interpretations for the case when the considered logic allows quantified number
restrictions and/or the constructor for the local reflexivity of a role, we
introduce a new notion called QS-interpretation, which is needed for obtaining
expected results. By adapting Hopcroft's automaton minimization algorithm and
the Paige-Tarjan algorithm, we give efficient algorithms for computing the
partition corresponding to the largest auto-bisimulation of a finite
interpretation.Comment: 42 page
Converting Instance Checking to Subsumption: A Rethink for Object Queries over Practical Ontologies
Efficiently querying Description Logic (DL) ontologies is becoming a vital
task in various data-intensive DL applications. Considered as a basic service
for answering object queries over DL ontologies, instance checking can be
realized by using the most specific concept (MSC) method, which converts
instance checking into subsumption problems. This method, however, loses its
simplicity and efficiency when applied to large and complex ontologies, as it
tends to generate very large MSC's that could lead to intractable reasoning. In
this paper, we propose a revision to this MSC method for DL SHI, allowing it to
generate much simpler and smaller concepts that are specific-enough to answer a
given query. With independence between computed MSC's, scalability for query
answering can also be achieved by distributing and parallelizing the
computations. An empirical evaluation shows the efficacy of our revised MSC
method and the significant efficiency achieved when using it for answering
object queries
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