Visual Query Language on Spatial Information (SIVQL) is one kind of visual query language based on the extension of Query by Example (QBE). It is a visual operation based on graphics or media object, such as point, li...Visual Query Language on Spatial Information (SIVQL) is one kind of visual query language based on the extension of Query by Example (QBE). It is a visual operation based on graphics or media object, such as point, line and area elements. In this paper, the relation calculation and query function of SIVQL have been studied and discussed by using set theory and relation algebra. The theory foundation of SIVQL has been investigated by the mathematical method. Finally, its application examples are also given with the specific information system.展开更多
According to the soundness and completeness of information in databases, the expressive form and the semantics of incomplete information are discussed in this paper. On the basis of the discussion, the current studies...According to the soundness and completeness of information in databases, the expressive form and the semantics of incomplete information are discussed in this paper. On the basis of the discussion, the current studies on incomplete data in relational databases are reviewed. In order to represent stochastic uncertainty in most general sense in the real world, probabilistic data are introduced into relational databases. An extended relational data model is presented to express and manipulate probabilistic data and the operations in relational algebra based on the extended model are defined in this paper.展开更多
Relation algebras give rise to partial algebras on maps, which are generalized to partial algebras on polymaps while preserving the properties of relation union and composition. A polymap is defined as a map with ever...Relation algebras give rise to partial algebras on maps, which are generalized to partial algebras on polymaps while preserving the properties of relation union and composition. A polymap is defined as a map with every point in the domain associated with a special set of maps. Polymaps can be represented as small subcategories of Set＊, the category of pointed sets. Map composition and the counterpart of relation union for maps are generalized to polymap composition and sum. Algebraic structures and categories of polymaps are investigated. Polymaps present the unique perspective of an algebra that can retain many of its properties when its elements （maps） are augmented with collections of other elements.展开更多
We generalize the concept -- dimension tree and the related results for monomial algebras to a more general case -- relations algebras A by bringing GrSbner basis into play. More precisely, we will describe the minima...We generalize the concept -- dimension tree and the related results for monomial algebras to a more general case -- relations algebras A by bringing GrSbner basis into play. More precisely, we will describe the minimal projective resolution of a left A-module M as a rooted ＇weighted＇ diagraph to be called the minimal resolution graph for M. Algorithms for computing such diagraphs and applications as well will be presented.展开更多
文摘Visual Query Language on Spatial Information (SIVQL) is one kind of visual query language based on the extension of Query by Example (QBE). It is a visual operation based on graphics or media object, such as point, line and area elements. In this paper, the relation calculation and query function of SIVQL have been studied and discussed by using set theory and relation algebra. The theory foundation of SIVQL has been investigated by the mathematical method. Finally, its application examples are also given with the specific information system.
文摘According to the soundness and completeness of information in databases, the expressive form and the semantics of incomplete information are discussed in this paper. On the basis of the discussion, the current studies on incomplete data in relational databases are reviewed. In order to represent stochastic uncertainty in most general sense in the real world, probabilistic data are introduced into relational databases. An extended relational data model is presented to express and manipulate probabilistic data and the operations in relational algebra based on the extended model are defined in this paper.
文摘Relation algebras give rise to partial algebras on maps, which are generalized to partial algebras on polymaps while preserving the properties of relation union and composition. A polymap is defined as a map with every point in the domain associated with a special set of maps. Polymaps can be represented as small subcategories of Set＊, the category of pointed sets. Map composition and the counterpart of relation union for maps are generalized to polymap composition and sum. Algebraic structures and categories of polymaps are investigated. Polymaps present the unique perspective of an algebra that can retain many of its properties when its elements （maps） are augmented with collections of other elements.
文摘We generalize the concept -- dimension tree and the related results for monomial algebras to a more general case -- relations algebras A by bringing GrSbner basis into play. More precisely, we will describe the minimal projective resolution of a left A-module M as a rooted ＇weighted＇ diagraph to be called the minimal resolution graph for M. Algorithms for computing such diagraphs and applications as well will be presented.
