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Deciding the SHOQ(D)-Satisfiability with a Fully Tiered Clause Group
Abstract
SHOQ(D) is one of the fundamental theories In Description Logics due to its support to concrete datatypes and named individuals. At present, deciding the satisfiability of SHOQ(D)-concepts is mainly completed by enhancing Tableau algorithm with blocking. However, there is still much to be desired in performance as there are tremendous description overlaps in completion forest, thus causing great spatial waste as a result. To tackle this problem, this paper presented a new approach to check the satisfiability of acyclic SHOQ(D)-concepts——FTC(Fully Tiered Clauses) algorithm. This calculus can make a direct judgement on the satisfiability of acyclic SHOQ(D)-concept by translating its description into a fully tiered clause group whose satisfiability is directly available, and reusing clauses to block unnecessary extensions. FTC algorithm eliminates description overlaps to the largest extent as it works on concept description directly. Therefore, FTC algorithm has notably better performance than Tableau by saving a lot of spatial costs.
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We present a dynamic description logic for representation and reasoning about actions, with an approach that embrace actions
into the description logic
ALCO@\mathcal {ALCO@}
. With this logic, description logic concepts can be used for describing the state of the world, and the preconditions and
effects of atomic actions; Complex actions can be modeled with the help of standard action operators, such as the test, sequence,
choice, and iteration operators; And both atomic actions and complex actions can be used as modal operators to construct formulas.
We develop a terminable and correct algorithm for checking the satisfiability of formulas. Based on the algorithm, many reasoning
tasks on actions are effectively carried out, including the realizability, executability, projection and planning problems.
A drawback which concept languages based on KL-ONE have is that all the terminological knowledge has to be defined on an abstract log ical level. In many applications, one would like to be able to refer to concrete domains and predicates on these domains when defin ing concepts. Examples for such concrete do mains are the integers, the real numbers, or also non-arithmetic domains, and predicates could be equality, inequality, or more complex pred icates. In the present paper we shall propose a scheme for integrating such concrete domains into concept languages rather than describing a particular extension by some specific concrete domain. We shall define a terminological and an assertional language, and consider the im portant inference problems such as subsump- tion, instantiation, and consistency. The for mal semantics as well as the reasoning algo rithms can be given on the scheme level. In con- trast to existing KL-ONE based systems, these algorithms are not only sound but also com plete. They generate subtasks which have to be solved by a special purpose reasoner of the concrete domain.
It is widely recognized today that the management of imprecision and
vagueness will yield more intelligent and realistic knowledge-based
applications. Description Logics (DLs) are a family of knowledge representation
languages that have gained considerable attention the last decade, mainly due
to their decidability and the existence of empirically high performance of
reasoning algorithms. In this paper, we extend the well known fuzzy ALC DL to
the fuzzy SHIN DL, which extends the fuzzy ALC DL with transitive role axioms
(S), inverse roles (I), role hierarchies (H) and number restrictions (N). We
illustrate why transitive role axioms are difficult to handle in the presence
of fuzzy interpretations and how to handle them properly. Then we extend these
results by adding role hierarchies and finally number restrictions. The main
contributions of the paper are the decidability proof of the fuzzy DL languages
fuzzy-SI and fuzzy-SHIN, as well as decision procedures for the knowledge base
satisfiability problem of the fuzzy-SI and fuzzy-SHIN.
As applications of description logics proliferate, efficient reasoning with knowledge bases containing many assertions becomes ever more important. For such cases, we developed a novel reasoning algorithm that reduces a SHIQ knowledge base to a disjunctive datalog program while preserving the set of ground conse- quences. Queries can then be answered in the resulting program while reusing existing and practically proven optimization techniques of deductive databases, such as join-order optimizations or magic sets. Moreover, we use our algorithm to derive precise data complexity bounds: we show that SHIQ is data complete for NP, and we identify an expressive fragment of SHIQ with polynomial data complexity.
Package-based Description Logics (P-DL) is a novel for- malism for modular ontologies. In P-DL, an ontology is composed of a collection of modules called packages. A package can partially reuse knowledge in other packages by a selective importing mech- anism. This paper investigates a sound and complete tableau-based reasoning algorithm for a P-DL language ALCPC, which extends ALC with acyclic concept importing between packages. The algo- rithm allows the reasoning process to be distributed based on local reasoning services offered by each module. The algorithm allows the reasoning process to be distributed based on local reasoning services offered by each module. Local tableaux associated with the ontol- ogy modules while physically separate, may conceptually overlap by communicating with each other via a set of messages. Our inves- tigation shows the algorithm can avoid several semantic difficulties associated with existing approaches, such as transitive subsumption propagation and inter-module unsatisfiability detection.
The Web Ontology Language OWL is a semantic markup language for publishing and sharing ontologies on the World Wide Web. OWL is developed as a vocabulary extension of RDF (the Resource Description Framework) and is derived from the DAML+OIL Web Ontology Language. This document contains a structured informal description of the full set of OWL language constructs and is meant to serve as a reference for OWL users who want to construct OWL ontologies.
Information exchange across various networks is made possible with the help of ontology. This will be possible with the development of a joint standard for specifying and exchanging ontologies. A standard named OIL is proposed to achieve the purpose. Different levels of complexity can be achieved as OIL is properly grounded in Web languages and its inner layers provides for efficient reasoning support based on FaCT. The application of ontologies is possible in the areas of knowledge management, Web commerce and e-business.
By introducing a dynamic dimension into the description logic, two kinds of dynamic description logics have been proposed in the literatures for representing and reasoning about knowledge of dynamic application domains. But both of them lack efficient decision algorithms. This paper presents a Tableau decision algorithm for the dynamic description logic D-ALCO. D-ALCO is a combination of the description logic ALCO, the dynamic logic, and an action theory based on the possible models approach. In D-ALCO, based on domain ontologies expressed in ALCO, atomic actions are described by specifying their preconditions and effects; With the help of standard action constructors of the dynamic logic, complex actions can be described also; Both atomic actions and complex actions are then used as modal operators in the construction of formulas. The Tableau decision algorithm for D-ALCO forms an elaborated combination of the Tableau algorithm for ALCO, the decision algorithm for propositional dynamic logic, and the embodiment of the possible models approach. The authors prove that the algorithm is terminating, sound and complete for deciding the satisfiability of D-ALCO formulas with the Open World Assumption. The algorithm is flexible and can be extended for more expressive dynamic description logics such as the D-ALCQO and the DALCQIO.
OWL DL, a new W3C ontology language recommendation, is based on the expressive description logic
. Although the ontology consistency problem for
is known to be decidable, up to now there has been no known “practical” decision procedure, that is, a goal-directed procedure that is likely to perform well with realistic ontology derived problems. We present such a decision procedure for
, a slightly more expressive logic than
, extending the well-known algorithm for
, which is the basis for several highly successful implementations.
The current research progresses and the existing problems of smantics representation of the semantic Web are analyzed. A kind of new fuzzy description logic FSHOIQ (fuzzy SHOIQ) for semantics representation of the semantic Web is presented, and the syntax and semantics of FSHOIQ are given. The fuzzy Tableaux of FSHOIQ is presented, then the ABox satisfiability reasoning algorithm of FSHOIQ based on the fuzzy Tableaux is presented, and the correctness of the satisfiability reasoning algorithm is proved. The TBox expansion and elimination methods are presented. It is proved that TBox subsumption reasoning problem may be translated into a satisfiability reasoning problem in FSHOIQ. Theoretical foundation for fuzzy knowledge representation and reasoning of the semantic Web is provided through FSHOIQ.
In order to use description logics (DLs) in an application, it is crucial to identify a DL that is sufficiently expressive
to represent the relevant notions of the application domain, but for which reasoning is still decidable. Two means of expressivity
required by many modern applications of DLs are concrete domains and general TBoxes. The former are used for defining concepts based on concrete qualities of their instances such as the weight, age, duration,
and spatial extension. The purpose of the latter is to capture background knowledge by stating that the extension of a concept
is included in the extension of another concept. Unfortunately, combining concrete domains with general TBoxes often leads
to DLs for which reasoning is undecidable. In this paper, we identify a general property of concrete domains that is sufficient
for proving decidability of DLs with both concrete domains and general TBoxes. We exhibit some useful concrete domains, most
notably a spatial one based on the RCC-8 relations that have this property. Then, we present a tableau algorithm for reasoning
in DLs equipped with concrete domains and general TBoxes.
One of the main characteristics of knowledge representation systems based on the description of concepts is the clear distinction between terminological and assertional knowledge. Although this characteristic leads to several computational and representational advantages, it usually limits the expressive power of the system. For this reason, some attempts have been done, allowing for a limited form of amalgamation between the two components and a more complex interaction between them. In particular, one of these attempts is based on letting the individuals to be referenced in the concept expressions. This is generally performed by admitting a constructor for building a concept from a set of enumerated individuals. In this paper we investigate the consequences of introducing this type of constructors in the concept description language. We also provide a complete reasoning procedure to deal with these constructors and we obtain some complexity results on it.
Ontologies are set to play a key role in the "Semantic Web", extending syntactic interoperability to semantic interoperability by providing a source of shared and precisely defined terms. DAML+OIL is an ontology language specifically designed for use on the Web; it exploits existing Web standards (XML and RDF), adding the familiar ontological primitives of object oriented and frame based systems, and the formal rigor of a very expressive description logic. The logical basis of the language means that reasoning services can be provided, both to support ontology design and to make DAML+OIL described Web resources more accessible to automated processes. 1
Ontologies are set to play a key role in the "Semantic Web" by providing a source of shared and precisely defined terms that can be used in descriptions of web resources. Reasoning over such descriptions will be essential if web resources are to be more accessible to automated processes. SHOQ(D) is an expressive description logic equipped with named individuals and concrete datatypes which has almost exactly the same expressive power as the latest web ontology languages (e.g., OIL and DAML). We present sound and complete reasoning services for this logic. 1
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