Temporal Fuzzy Description Logic Based On Time Interval Relationship And Its Reasoning

Based on the representation of object knowledge，Description Logic is a kind offormal tools，which is a subset of first order predicate and a logical formula aggregateof conceptual knowledge for describing and reasoning. Expect for representation ofknowledge，Description Logic also applies on many fields，it is considered as themost important normalized form of knowledge representation which is centering onthe object. The important features of Description Logic is the strong expressive powerand decidability，it ensures the termination of reasoning algorithm and returns theright results. At first，Description Logic is used for representing the static konwledge，given that the changing on tense and action，and keeping the simplicity of thelanguage，so we need to extend it by increasing modal operator naturally. As is knownto all，we can make the system more complex when we only hybird the simplysystems. In fist chapter of the paper，it will present the researchers’ study on theDescription Logic’s extension by increasing operators(like temporal，fuzzy，dynamicand so on) and its correctness of the decidable and reasoning algorithm.The most information have tense property and fuzzy and inprecise in the world，we can get the result that the traditional Fuzzy Description Logic lacks expressivepower in imprecision knowledge which is changing by time from analyzing theTemporal logic and Fuzzy logic. Aimed at this problem，the paper proposes a logic oftemporal fuzzy Description Logic based on temporal interval relationship namedTFDL(IntervalAllen). Compared with the fuzzy Description Logic，it adds tenseoperator and uses the Allen interval relationship to represent the temporal intervalrelationship，combines with the computing of Vague sets. It’s a extension on tense offuzzy Description Logic—FALC，it can express the knowledge which has temporalrelationship， besides the problems which fuzzy Description Logic can solve.Meanwhile it also enhances expressive power in representing the temporalrelationship of fuzzy knowledge.The main research works of the paper are as follows:(1) It gives TFDL(IntervalAllen)’s syntax， semantics and knowledge base representation. The general formulas of TFDL(IntervalAllen) reflected temporal andfuzzy through superscript and subscript， and we interpret the Allen intervalrelationship through the semantic and define the quad to interpret the concept andconcept’s operation in TFDL(IntervalAllen).Then gives the sementic interpretation onABox and TBox and PBox respectively.(2) Based on the TFDL(IntervalAllen)’s semantic interpretations，we study someimportant properties of TFDL(IntervalAllen). We put forward ten basic properties onthe concept equivalence and nine ponens on the entailment relation，and we alsodiscuss its rationality in detail and give its formal proofs.(3) Based on the satisfiability algorithm Tableaux of fuzzy description logic，weput forward satisfiability decidable algorithm of concepts in TFDL(IntervalAllen)，andconstruct the clash by introducing the Fuzzy Conjugate，especially considering thetemporal relationships. Then we prove the correctness，soundness and completenessof this algorithm. In addition，we make a strict proof of the transformation fromconcept fuzzy inclusion，concept fuzzy equivalent and concept disjoint to the decidingof conceptual satisfiability respectively.