9,856 research outputs found
The complexity of existential quantification in concept languages
Much of the research on concept languages, also called terminological languages, has focused on the computational complexity of subsumption. The intractability results can be divided into two groups. First, it has been shown that extending the basic language FL- with constructs containing some form of logical disjunction leads to co-NP-hard subsumption problems. Second, adding negation to FL- makes subsumption PSPACE-complete. The main result of this paper is that extending FL- with unrestricted existential quantification makes subsumption NP-complete. This is the first proof of intractability for a concept language containing no construct expressing disjunction--whether explicitly or implicitly. Unrestricted existential quantification is therefore, alongside disjunction, a source of computational complexity in concept languages
The Vadalog System: Datalog-based Reasoning for Knowledge Graphs
Over the past years, there has been a resurgence of Datalog-based systems in
the database community as well as in industry. In this context, it has been
recognized that to handle the complex knowl\-edge-based scenarios encountered
today, such as reasoning over large knowledge graphs, Datalog has to be
extended with features such as existential quantification. Yet, Datalog-based
reasoning in the presence of existential quantification is in general
undecidable. Many efforts have been made to define decidable fragments. Warded
Datalog+/- is a very promising one, as it captures PTIME complexity while
allowing ontological reasoning. Yet so far, no implementation of Warded
Datalog+/- was available. In this paper we present the Vadalog system, a
Datalog-based system for performing complex logic reasoning tasks, such as
those required in advanced knowledge graphs. The Vadalog system is Oxford's
contribution to the VADA research programme, a joint effort of the universities
of Oxford, Manchester and Edinburgh and around 20 industrial partners. As the
main contribution of this paper, we illustrate the first implementation of
Warded Datalog+/-, a high-performance Datalog+/- system utilizing an aggressive
termination control strategy. We also provide a comprehensive experimental
evaluation.Comment: Extended version of VLDB paper
<https://doi.org/10.14778/3213880.3213888
A Parameterized Complexity View on Description Logic Reasoning
Description logics are knowledge representation languages that have been
designed to strike a balance between expressivity and computational
tractability. Many different description logics have been developed, and
numerous computational problems for these logics have been studied for their
computational complexity. However, essentially all complexity analyses of
reasoning problems for description logics use the one-dimensional framework of
classical complexity theory. The multi-dimensional framework of parameterized
complexity theory is able to provide a much more detailed image of the
complexity of reasoning problems.
In this paper we argue that the framework of parameterized complexity has a
lot to offer for the complexity analysis of description logic reasoning
problems---when one takes a progressive and forward-looking view on
parameterized complexity tools. We substantiate our argument by means of three
case studies. The first case study is about the problem of concept
satisfiability for the logic ALC with respect to nearly acyclic TBoxes. The
second case study concerns concept satisfiability for ALC concepts
parameterized by the number of occurrences of union operators and the number of
occurrences of full existential quantification. The third case study offers a
critical look at data complexity results from a parameterized complexity point
of view. These three case studies are representative for the wide range of uses
for parameterized complexity methods for description logic problems.Comment: To appear in the Proceedings of the 16th International Conference on
Principles of Knowledge Representation and Reasoning (KR 2018
EquiX---A Search and Query Language for XML
EquiX is a search language for XML that combines the power of querying with
the simplicity of searching. Requirements for such languages are discussed and
it is shown that EquiX meets the necessary criteria. Both a graphical abstract
syntax and a formal concrete syntax are presented for EquiX queries. In
addition, the semantics is defined and an evaluation algorithm is presented.
The evaluation algorithm is polynomial under combined complexity.
EquiX combines pattern matching, quantification and logical expressions to
query both the data and meta-data of XML documents. The result of a query in
EquiX is a set of XML documents. A DTD describing the result documents is
derived automatically from the query.Comment: technical report of Hebrew University Jerusalem Israe
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
The Complexity of Satisfiability for Sub-Boolean Fragments of ALC
The standard reasoning problem, concept satisfiability, in the basic
description logic ALC is PSPACE-complete, and it is EXPTIME-complete in the
presence of unrestricted axioms. Several fragments of ALC, notably logics in
the FL, EL, and DL-Lite family, have an easier satisfiability problem;
sometimes it is even tractable. All these fragments restrict the use of Boolean
operators in one way or another. We look at systematic and more general
restrictions of the Boolean operators and establish the complexity of the
concept satisfiability problem in the presence of axioms. We separate tractable
from intractable cases.Comment: 17 pages, accepted (in short version) to Description Logic Workshop
201
- …