402 research outputs found
Reasoning with Individuals for the Description Logic SHIQ
While there has been a great deal of work on the development of reasoning
algorithms for expressive description logics, in most cases only Tbox reasoning
is considered. In this paper we present an algorithm for combined Tbox and Abox
reasoning in the SHIQ description logic. This algorithm is of particular
interest as it can be used to decide the problem of (database) conjunctive
query containment w.r.t. a schema. Moreover, the realisation of an efficient
implementation should be relatively straightforward as it can be based on an
existing highly optimised implementation of the Tbox algorithm in the FaCT
system.Comment: To appear at CADE-1
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
Optimizing Description Logic Reasoning for the Service Matchmaking and Composition
The Semantic Web is a recent initiative to expose semantically rich information associated with Web resources to build more intelligent Web-based systems. Recently, several projects have embraced this vision and there are several successful applications that combine the strengths of the Web and of semantic technologies. However, Semantic Web still lacks a technology, which would provide the needed scalability and integration with existing infrastructure. In this paper we present our ongoing work on a Semantic Web repository, which is capable of addressing complex schemas and answer queries over ontologies with large number of instances. We present the details of our approach and describe the underlying architecture of the system. We conclude with a performance evaluation, which compares the current state-of-the-art reasoners with our system
Description Logics as Ontology Languages for the Semantic Web
The vision of a Semantic Web has recently drawn considerable attention, both from academia and industry. Description logics are often named as one of the tools that can support the Semantic Web and thus help to make this vision reality. In this paper, we describe what description logics are and what they can do for the Semantic Web. Descriptions logics are very useful for defining, integrating, and maintaining ontologies, which provide the Semantic Web with a common understanding of the basic semantic concepts used to annotate Web pages. We also argue that, without the last decade of basic research in this area, description logics could not play such an important rˆole in this domain
Extending the Description Logic Ï„EL(deg) with Acyclic TBoxes
In a previous paper, we have introduced an extension of the lightweight Description Logic EL that allows us to define concepts in an approximate way. For this purpose, we have defined a graded membership function deg, which for each individual and concept yields a number in the interval [0; 1] expressing the degree to which the individual belongs to the concept. Threshold concepts C~t for ~ 2 ∈ {, ≥} then collect all the individuals that belong to C with degree ~ t. We have then investigated the complexity of reasoning in the Description Logic τEL(deg), which is obtained from EL by adding such threshold concepts. In the present paper, we extend these results, which were obtained for reasoning without TBoxes, to the case of reasoning w.r.t. acyclic TBoxes. Surprisingly, this is not as easy as might have been expected. On the one hand, one must be quite careful to define acyclic TBoxes such that they still just introduce abbreviations for complex concepts, and thus can be unfolded. On the other hand, it turns out that, in contrast to the case of EL, adding acyclic TBoxes to τEL(deg) increases the complexity of reasoning by at least on level of the polynomial hierarchy
Subsumption algorithms for concept languages
We investigate the subsumption problem in logic-based knowledge representation languages of the KL-ONE family and give decision procedures. All our languages contain as a kernel the logical connectives conjunction, disjunction, and negation for concepts, as well as role quantification. The algorithms are rule-based and can be understood as variants of tableaux calculus with a special control strategy. In the first part of the paper, we add number restrictions and conjunction of roles to the kernel language. We show that subsumption in this language is decidable, and we investigate sublanguages for which the problem of deciding subsumption is PSPACE-complete. In the second part, we amalgamate the kernel language with feature descriptions as used in computational linguistics. We show that feature descriptions do not increase the complexity of the subsumption problem
Reasoning with Forest Logic Programs and f-hybrid Knowledge Bases
Open Answer Set Programming (OASP) is an undecidable framework for
integrating ontologies and rules. Although several decidable fragments of OASP
have been identified, few reasoning procedures exist. In this article, we
provide a sound, complete, and terminating algorithm for satisfiability
checking w.r.t. Forest Logic Programs (FoLPs), a fragment of OASP where rules
have a tree shape and allow for inequality atoms and constants. The algorithm
establishes a decidability result for FoLPs. Although believed to be decidable,
so far only the decidability for two small subsets of FoLPs, local FoLPs and
acyclic FoLPs, has been shown. We further introduce f-hybrid knowledge bases, a
hybrid framework where \SHOQ{} knowledge bases and forest logic programs
co-exist, and we show that reasoning with such knowledge bases can be reduced
to reasoning with forest logic programs only. We note that f-hybrid knowledge
bases do not require the usual (weakly) DL-safety of the rule component,
providing thus a genuine alternative approach to current integration approaches
of ontologies and rules
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