The Research On Several Issues Of Description Logics

In recent years, Description logics (DLs) have become a central topic in ArtificialIntelligence. Generally, DLs are a class of knowledge representation languages, and canmodel an application domain of interest by a structured and formally well-understood way.Moreover, DLs can be used in various areas, for example, Semantic Web, Ontologies,software engineering. However, due to the represented formalism and complexity of thedescription logic itself, DL cannot well model a great deal of real-world problems. How toconstruct a description logic system with strong expressive power and high efficiency ofreasoning has not yet been well solved up to now.This paper studies the description logics with higher expressive power, and thedescription logics with lower reasoning complexities. We focus on investigating theknowledge compilation for description logics, non-classical description logics, anddescription logic programs, and have done the systematic and in-depth study on the inherentdefects of these methods, and carried out a series of studies by focusing on how to increasethe expressive power and enhance the reasoning efficiency of description logics. We haveproposed knowledge compilation for description logic based on concept extension rule andbased on concept Shannon expansion, knowledge compilation for description logic based onconcept implicate tree, rough description logic++and rough description logic program,interval-based possibilistic description logic and possibilistic description logic program,paraconsistent fuzzy description logics. The main contribution of this paper and researchresults are as follows:1) We have done a comprehensive overview on the state of the art of the descriptionlogics and non-classical description logics, made an analysis and discussion of the currentdevelopment trends and problems faced in these areas. Morevoer, we have made a briefsurvey of the research development of the knowledge compilations and logic programs, andanalyzed and discussed the current situation and existing problems. The discussion andanalysis of these topics have laid a theoretical foundation for future research work.2) We have proposed three knowledge compilation methods for description logics inorder to enhance the reasoning efficiency. Firstly, we presented knowledge compilationmethod for description logic based on concept extension rule, and compiled an ALC conceptwith some restriction into an equivalence EPCCCL concept, and proved thatsatisfiabiliy-testing and subsumption-testing can be done in linear time in the size of thecompiled concept. If the concept is very similar to EPCCCL concept, then this method is veryefficient. Secondly, we provided knowledge compilation method for description logic based on concept Shannon expansion, which can be regarded as the dual method for the first method.This method can translate any ALC concept into an equivalent DPLC concept, for which thecomplexity of reasoning is liner time in the size of the compiled concept. If the concept isvery similar to DPLC concept, then this method is better than the first method. Finally, weproposed knowledge compilation method for description logic based onconcept implicate tree,and transformed any ALC concept into an equivalent concept implicate tree, and proved thatthe queries are computable in linear time in the size of the query. If the size of the compiledconcept is very large, then this method is more effective than other methods.3) We have proposed rough description logic++in order to enhance the reasoningefficiency for rough description logics.++is a tractable rough description logic, and anextension of description logic++and rough set theory. Firstly, we defined the syntax andsemantics of++, then we provided some algorithms to deal with the reasoning problemsfor++, finally, we proved that the complexity of++reasoning was polynominaltime. In a word,++can represent and reason on uncertain information, moreover, thereasoning can be done in polynominal time.4) We proposed interval-based possibilistic description logic in order to incresase theexpressive power. Interval-based possibilistic description logic extended description logicwith an interval-based possibilistic logic, and used an interval to represent the inaccuratedegrees associated with DL axioms, instead of a number between0and1. Firstly, we definedthe syntax and semantics, and then we provided some properties, finally, we presented threereasoning problems and presented some algorithms to solve these reasoning problems.Interval-based possibilistic description logic can represent and reason on uncertaininformation, and can deal with inconsistent knowledge base.5) We have proposed two description logic programs in order to increase the expressivepower.①We presented rough description logic program, which can represent uncertain andincomplete information, and can deal with monotonic reasoning and non monotonic reasoningat the same time. Firstly, we defined the syntax of rough description logic program, and thenwe presented the semantics of rough description logic program, finally we provided somesemantic properties of rough description logic program under the answer set semantics.②Weproposed tightly coupled possibilistic description logic programs under the possibilisticanswer set semantics, which are a tight integration of disjunctive logic programs under theanswer set semantics, possibilistic logics and possibilistic description logics. First of all, wedefined the syntax and semantics of possibilistic description logic program, and then wepresented some semantic properties, finally, we defined some reasoning problems andprovided reasoning algorithms for possibilistic description logic program. In a word,possibilistic description logic program can model uncertain, incomplete and inconsistent information, and can do monotonic and non monotonic reasoning.6) We have proposed paraconsistent fuzzy description logic in order to increase theexpressive power. Paraconsistent fuzzy description logic, which is a combination of fuzzydescription logic and paraconsistent description logic, used fuzzy logic to represent fuzzyinformation, and used paraconsistent logic to represent inconsistent information, and canreason on inconsistent knowledge base. First of all, we defined the syntax, semantics andreasoning problems, and then we presented the paraconsistent fuzzy tableaux algorithm basedon constraint propagation rules and proved the completeness of the algorithm, finally, weprovided some relation between paraconsistent fuzzy description logic and fuzzy descriptionlogic. Therefore, paraconsistent fuzzy description logic has strong expressive power andhigher efficiency of reasoning, and better compatibility, and lays a theoretical foundation forthe representation and reasoning of paraconsistent fuzzy information in the Semantic Web.