315 research outputs found
Reasoning over Ontologies with Hidden Content: The Import-by-Query Approach
There is currently a growing interest in techniques for hiding parts of the
signature of an ontology Kh that is being reused by another ontology Kv.
Towards this goal, in this paper we propose the import-by-query framework,
which makes the content of Kh accessible through a limited query interface. If
Kv reuses the symbols from Kh in a certain restricted way, one can reason over
Kv U Kh by accessing only Kv and the query interface. We map out the landscape
of the import-by-query problem. In particular, we outline the limitations of
our framework and prove that certain restrictions on the expressivity of Kh and
the way in which Kv reuses symbols from Kh are strictly necessary to enable
reasoning in our setting. We also identify cases in which reasoning is possible
and we present suitable import-by-query reasoning algorithms
Expressive probabilistic description logics
AbstractThe work in this paper is directed towards sophisticated formalisms for reasoning under probabilistic uncertainty in ontologies in the Semantic Web. Ontologies play a central role in the development of the Semantic Web, since they provide a precise definition of shared terms in web resources. They are expressed in the standardized web ontology language OWL, which consists of the three increasingly expressive sublanguages OWL Lite, OWL DL, and OWL Full. The sublanguages OWL Lite and OWL DL have a formal semantics and a reasoning support through a mapping to the expressive description logics SHIF(D) and SHOIN(D), respectively. In this paper, we present the expressive probabilistic description logics P-SHIF(D) and P-SHOIN(D), which are probabilistic extensions of these description logics. They allow for expressing rich terminological probabilistic knowledge about concepts and roles as well as assertional probabilistic knowledge about instances of concepts and roles. They are semantically based on the notion of probabilistic lexicographic entailment from probabilistic default reasoning, which naturally interprets this terminological and assertional probabilistic knowledge as knowledge about random and concrete instances, respectively. As an important additional feature, they also allow for expressing terminological default knowledge, which is semantically interpreted as in Lehmann's lexicographic entailment in default reasoning from conditional knowledge bases. Another important feature of this extension of SHIF(D) and SHOIN(D) by probabilistic uncertainty is that it can be applied to other classical description logics as well. We then present sound and complete algorithms for the main reasoning problems in the new probabilistic description logics, which are based on reductions to reasoning in their classical counterparts, and to solving linear optimization problems. In particular, this shows the important result that reasoning in the new probabilistic description logics is decidable/computable. Furthermore, we also analyze the computational complexity of the main reasoning problems in the new probabilistic description logics in the general as well as restricted cases
Type-elimination-based reasoning for the description logic SHIQbs using decision diagrams and disjunctive datalog
We propose a novel, type-elimination-based method for reasoning in the
description logic SHIQbs including DL-safe rules. To this end, we first
establish a knowledge compilation method converting the terminological part of
an ALCIb knowledge base into an ordered binary decision diagram (OBDD) which
represents a canonical model. This OBDD can in turn be transformed into
disjunctive Datalog and merged with the assertional part of the knowledge base
in order to perform combined reasoning. In order to leverage our technique for
full SHIQbs, we provide a stepwise reduction from SHIQbs to ALCIb that
preserves satisfiability and entailment of positive and negative ground facts.
The proposed technique is shown to be worst case optimal w.r.t. combined and
data complexity and easily admits extensions with ground conjunctive queries.Comment: 38 pages, 3 figures, camera ready version of paper accepted for
publication in Logical Methods in Computer Scienc
Selecting Ontology Entailments for Presentation to Users
Peer reviewedPreprin
Conjunctive Query Answering for the Description Logic SHIQ
Conjunctive queries play an important role as an expressive query language
for Description Logics (DLs). Although modern DLs usually provide for
transitive roles, conjunctive query answering over DL knowledge bases is only
poorly understood if transitive roles are admitted in the query. In this paper,
we consider unions of conjunctive queries over knowledge bases formulated in
the prominent DL SHIQ and allow transitive roles in both the query and the
knowledge base. We show decidability of query answering in this setting and
establish two tight complexity bounds: regarding combined complexity, we prove
that there is a deterministic algorithm for query answering that needs time
single exponential in the size of the KB and double exponential in the size of
the query, which is optimal. Regarding data complexity, we prove containment in
co-NP
Metamodeling and metaquerying in OWL 2 QL
OWL 2 QL is a standard profile of the OWL 2 ontology language, specifically tailored to Ontology-Based Data Management. Inspired by recent work on higher-order Description Logics, in this paper we present a new semantics for OWL 2 QL ontologies, called Metamodeling Semantics (MS), and show that, in contrast to the official Direct Semantics (DS) for OWL 2, it allows exploiting the metamodeling capabilities natively offered by the OWL 2 punning. We then extend unions of conjunctive queries with both metavariables, and the possibility of using TBox atoms, with the purpose of expressing meaningful metalevel queries. We first show that under MS both satisfiability checking and answering queries including only ABox atoms, have the same complexity as under DS. Second, we investigate the problem of answering general metaqueries, and single out a new source of complexity coming from the combined presence of a specific type of incompleteness in the ontology, and of TBox axioms among the query atoms. Then we focus on a specific class of ontologies, called TBox-complete, where there is no incompleteness in the TBox axioms, and show that general metaquery answering in this case has again the same complexity as under DS. Finally, we move to general ontologies and show that answering general metaqueries is coNP-complete with respect to ontology complexity, Π2p-complete with respect to combined complexity, and remains AC0 with respect to ABox complexity
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