Abstract—This paper presents some concepts of Generalized Positive Boolean Dependencies (GPBDs) in relational database. Positive formulas means logic formulas formed by variables, constants 0/1 which is true if all variables are true. In fact, it shows that relational database expanded by Generalized Positive Dependencies can process complex database constraints, and traditional dependency is one case of Generalized Positive Dependencies. The first section of this paper is about some basic concepts and the need of Generalized Positive Dependencies in particular, major results involved in this dependency such as equivalence theorem among three types of reasoning for all logical dependency classes: reasoning in the world of all relations, reasoning in the world of 2-tuple relations and reasoning of propositional logic. It also shows that functional dependencies, strong, weak and dual dependencies are ones of cases of Generalized Positive Boolean dependencies. Through equivalence theorem, membership problem can be solved. It defines whether Generalized positive Boole dependency can be derived from set of Generalized positive Boole dependencies or not. The last section presents an algorithm to solve the above problems in general.

Index Terms—Positive boolean dependency, generalized positive boolean dependencies; equivalence theorem

Luong Nguyen Hoang Hoa is with the Department if Information Technology, Posts and Telecommunication Institute of Technology,Vietnam (hoaln79@gmail.com)

Cite: Luong Nguyen Hoang Hoa, "Some Results concerning Generalized Positive Boolean Dependencies in relational Database," International Journal of Computer and Electrical Engineering vol. 3, no. 6, pp. 779-783, 2011.