SATURATEDNESS AND A HIERARCHY OF APPROXIMATE IDENTITIES

In this paper, 'identity' is eventually considered to be determined by a specified collection of 'properties' represented extensionally by subsets. Generally, the collection may contain fuzzy subsets representing vague properties, thus rendering vagueness to the concept of identity. Saturatedness condition, which in essence is a portion of Leibniz's principle of identity, has been dealt with in some detail. A hierarchy of identities is obtained. This hierarchy also indicates some relationship between the concepts 'identity' and 'property'. Some applications of the results to the modelling of indistinguishability in information systems have been indicated.