Lipski's approach to incomplete information data bases restated and generalized in the setting of Zadeh's possibility theory

摘要

The main purpose of this paper is to make clear the connection between Lipski's approach to incomplete information databases and Zadeh's possibility theory which both appeared recently, quite simultaneously, but in different contexts. Lipski's approach is extended by introducing [0, 1]-valued levels of possibility in order to take into account the fact that our incomplete knowledge about properties of objects in databases may be based on soft (non-binary) information or on statistical-like data. Moreover, possibility theory, enlarged by the introduction of the concept of necessity, seems easier to manipulate than the semantics of usual modal logic used by Lipski. The problems of dependencies, of “yes-no” queries or of queries involving the cardinalities of specified sets when available information is incomplete are considered. Two illustrative examples are dealt with.