Research On Integrating Description Logics And Rules

Semantic web has received wide spread attention of the researchers since it was proposed in 1998. In 2000, the layered architecture of the Semantic web, which is called the semantic web layer cake, was recommended on the XML International Conference. The layer cake consists of seven layers: Unicode and URIs are the most foundamental layer of this architecture, and layer of XML and namespace, RDF layer, ontological layer, logical layer (rule layer), layer of proof and layer of trust are situated in turn on this layer cake. In the view of implementation, integration of each layer is one of the most important issues of the semantic web. Especially, the integration of the ontological layer and rule layer has become one of the important tasks of the semantic web.The benefits of integrating onlogical layer and rule layer are listed below:Firstly, it is well known that the logical foundation of the most commonly used ontology representation language the Web Ontology Language is description logics (DLs) and they have many knowledge representation limitations: First, in general, description logics are used to represent structural knowledge and it is difficult to represent other kinds of knowledge such as statement. Second, only unary and binary predicates are allowed to occur in DLs and the family of description logics is lack of mechanism to represent n-arity(n>2) predicates. Third, description logics are based on open world assumption and reasoning in DLs is monotonic. However, nonmonotonic reasoning such as default reasoning is essential to reasoning tasks such as query answering in the semantic web. Secondly, the power of query answering in the ontology languages is very limited and the combination of rules with ontologies can improve their ability to answer queries. Thirdly, currently, the mechanism of data processing and handling of relational database are very stable. However, the transformation from description logics to relational database is not very easy, but the same transformation from rules to database is much easier. Fourthly, in the semantic web service, ontologies are used to represent input and output of the services and rules are for temporary characteristics. Seamless integration of them will accomplish the semantic web services more perfectly.As it was said above, the logical foundation of ontology layer is description logics (DLs). So, Combination of the ontology layer and rule layer is implemented by integrating description logics with rules.Main challenge of integrating description logics with rules comes from the decidability of reasoning in hybrid knowledge base. The direct combination of decidable fragment of these two knowledge representation formalisms can easily lead to undecidability because the decidability of these two kinds of knowledge representation comes from very different angles. In fact, the decidability of description logics relies on the sublanguage's tree-model-property whereas the unrestricted use of variables could lead to undecidability in logic programs. Besides the decidability issue, if the rule part of combined system is nonmonotonic one, there also exist semantic issues, i.e. the semantic of description logic is interpreted under open world assumption while the rules are interpreted under closed world assumption. Thus defining semantic for this kind of integrated knowledge base is one of the most important tasks of the implementation of combinations.Along with the development of semantic web, many approaches to integrate description logics with rules have been proposed, such as DLP, SWRL, CARIN, AL-Log, ALCpu etc. Theses approaches all have some limitations on their expressive power and reasoning ability. In this paper, we will study the description logics and rules in the background of the semantic web and contribute following research works:(1)Integration of description logics with monotonic rules: we give the hybrid knowledge base system SHOIQ-Datalog which is the syntactical extension of the CARIN system to DL language SHOIQ. Intuitively, the SHOIQ-Datalog knowledge base is divided into two components: DL component and rule component. The DL component is described by DL language SHOIQ while the rule component consists of a set of hybrid datalog rules, which are datalog rules allowing the DL concept and roles to occur in their rule body. Thus, the communication of two components can be implemented by these DL concepts and roles occurring in the datalog. To preserve decidability, we impose the so-called DL-safe condition to the hybrid rules. That can be described as follows: all variables occurring in the hybrid rule must occur in the non-dl atoms in rule body. We use the goal-driven backward reasoning algorithm for the system which is the combination of Tableau procedure for DL language SHOIQ and SLD derivation for the hybrid rules. More precisely, the algorithm use SLD derivation to given query clause and obtain sets of DL assertions. Then, transform the role assertions to concept assertions using syntactic transformation rules. At last, instance checking for the concept assertion would be precede with the Tableau algorithm. The time complexity of our reasoning algorithm is NExpTime-Complete. In comparation with the CARIN system, our system not only improved the expressive power of the hybrid system but also provided more effective reasoning algorithm.(2)Integration of description logics and nonmonotonic rules: we describe a hybrid system SHOIQ-N-Datalog which is nonmonotic extension of the SHOIQ-Datalog system. Because the rule component of SHOIQ-Datalog is datalog program, nonmonotonic reasoning which is essential to the semantic web cannot be supported in SHOIQ-Datalog system. In SHOIQ-N-Datalog system, we use Datalog? program to construct the rule component of the knowledge base, i.e. we allow the negation as failure not to occur in the rule body of the rule part in the system. However, the semantic issue arises from the open world assumption in DLs and the closed world assumption of Datalog? program. In the semantic definition of the SHOIQ-N-Datalog system, we use the interpretation of the DL component to reduce the rule component and then define nonmonotonic semantic for the remaining non-dl literals. Thus, all the DL concepts and roles in the DL component are interpreted in open world assumption whereas the non-dl literals in rule component are interpreted in closed world assumption. To remain decidability of reasoning, we impose following safeness condition to the rule component: every variables occurring in the rule must occur in the positive non-dl literal in the rule body. Then, we develop an algorithm which is combination of the SLDNF resolution and Tableau decision procedure to answer queries over the knowledge base. In comparion with the SHOIQ-Datalog system described above, SHOIQ-N-Datalog system enhanced the knowledge representation of the semantic web providing more expressive power on the rule component of hybrid knowledge base system.Summing up, our work not only provided approaches enhancing hybrid knowledge base of integration of description logics and rules but also improved the reasoning efficiency by reducing time complexity of reasoning algorithm. SHOIQ-Datalog system provided mechanism to combine OWL-DL language and datalog rules by extending the CARIN system to DL language SHOIQ. In addition, the reasoning algorithm we developed is more effective one compared with CARIN. SHOIQ-N-Datalog system improved the expressive power of integrated system further by extending the rule part to Datalog? program. Thus, it provided theoretical paradigms towards nonmonotonic reasoning in the semantic web.