A Logical Explication of the Concepts of Incomplete and Uncertain Information

Abstract

Discovery of elementary knowledge and its constituents, i.e. information contained in objects of reality is realized through asking questions including certain aspects called attributes in this paper. We describe a fragment of a discovered reality as an information system (cf. Pawlak [1,3,4]), which consists of the universum U of all the objects of this reality we are concerned with, and of a set A of attributes understood as functions each of which assigns to every object of U 1) a value of given attribute belonging to A or 2) an interval of approximate values of this attribute, i.e. an established set of possible values of this attribute. From the point of view of the cognitive agent and his knowledge of the attributes of this information system, such system is a complete system when the values of all its attributes for any objects are known, contrary to incomplete system, in which value or, respectively, set of values for an attribute are unknown or are not available, though at the same time the only possible. A complete system in the case of 1) is called by us exact and in the case of 2) is called by us approximate. An incomplete system is called by us inexact, or uncertain, or vague, in the case of 1) or strongly uncertain, or strongly vague in the case of 2).