Research On Representation And Reasoning Of Fuzzy Spatio-Temporal Knowledge Based On Description Logics

With the development and application of the Semantic Web,description logics,which are characterized by easy-to-understand formal representation and sound reasoning mechanism,have become a logical foundation of knowledge representation and reasoning in the Semantic Web.Description logics are a decidable subset of first-order predicate logic,which play an important role in the real application of the Semantic Web.In the real world applications,many fields contain a large number of fuzzy spatio-temporal knowledge(static fuzzy spatio-temporal knowledge and dynamic fuzzy spatio-temporal knowledge).With a large amount of fuzzy spatio-temporal knowledge and many corresponding applications being incorporated into the Semantic Web,description logics become an effective method to solve the representation and reasoning problem of fuzzy spatio-temporal knowledge.The research of fuzzy spatio-temporal extension of description logics will provide a feasible solution for the realization of the automatic reasoning of fuzzy spatio-temporal knowledge in the Semantic Web and many fields.However,there is little research on the representation and reasoning of fuzzy spatio-temporal knowledge based on description logics.How to extend description logics to make it able to have the ability to represent and reason fuzzy spatio-temporal knowledge is an important research problem to be solved in the Semantic Web and many fields.To this end,in this paper,representation and reasoning of fuzzy spatio-temporal knowledge based on description logics are systematically studied.In-depth studies on the formal representation of fuzzy spatio-temporal knowledge,reasoning of static fuzzy spatio-temporal knowledge,and reasoning of dynamic fuzzy spatio-temporal knowledge are presented in this paper.The innovative contributions of the paper are as follows:(1)In view of the problem of the formal representation of fuzzy spatio-temporal knowledge in the real spatio-temporal application,a representation model(framework)of fuzzy spatio-temporal objects and their topological relations is proposed.Firstly,based on fuzzy spatial objects,the formal representation model of fuzzy spatio-temporal objects is given,and the graphical representation of the model is also given.Then,based on RCC8 model,a representation model for identifying basic(static)fuzzy topological relations between fuzzy spatio-temporal objects is proposed.This model covers 6 kinds of topological relations between fuzzy spatio-temporal objects,namely among moving fuzzy points,among moving fuzzy point to moving fuzzy line,among moving fuzzy point to moving fuzzy region,among moving fuzzy lines,among moving fuzzy line to moving fuzzy region,and among moving fuzzy regions.Moreover,on the basis of the basic fuzzy topological relations,a complex(dynamic)fuzzy topological relation(predicate)model is proposed,which is used to represent the evolution of the basic fuzzy topological relations over time.Finally,the topological relations between fuzzy spatio-temporal objects are integrated into the database query language so as to realize the query of fuzzy spatio-temporal objects.(2)In view of the problem of representation and reasoning of static fuzzy spatio-temporal domain knowledge in the environment of the Semantic Web,a fuzzy spatial description logic called f-ALC(S)is proposed.Firstly,a fuzzy spatial concrete domain S based on fuzzy RCC topological relations is defined,and the concrete domain S is proved to be admissible.Secondly,the admissible concrete domain S is introduced to fuzzy description logic f-ALC,and a fuzzy spatial description logic f-ALC(S)supporting inferences of fuzzy spatial relations is proposed.The formal definitions of syntax,semantics and knowledge base of the f-ALC(S)are also given.Furthermore,a basic reasoning problem of f-ALC(S)is discussed and a tableau algorithm for determining the consistency of f-ALC(S)ABox w.r.t an empty TBox is proposed.The decision process of the tableau algorithm is further displayed by a specific example.Finally,the termination,soundness,and completeness of the tableau algorithm are shown and the complexity of the reasoning problem is analyzed to be PSPACE-complete.(3)In view of the problem of representation and reasoning of dynamic fuzzy spatio-temporal domain knowledge in the environment of the Semantic Web,based on temporal extension of fuzzy spatial description logic f-ALC(S),a fuzzy spatio-temporal description logic called f-ALC(S)-LTL is proposed.Firstly,by introducing the different components of f-ALC(S)into linear temporal logic LTL,the formal definitions of concept syntax,formula syntax,and semantic interpretation are given.Secondly,the Hintikka structure of f-ALC(S)-LTL formula is defined.Then,based on the reasoning mechanisms of LTL and f-ALC(S),a tableau algorithm for determining satisfiability problem of f-ALC(S)-LTL formula is proposed.Finally,with the help of Hintikka structure,the termination,soundness,and completeness of the tableau algorithm is proved,and the complexity of the satisfiability problem of f-ALC(S)-LTL formula is analyzed to be EXPTIME-complete.