  In this research, a general theoretical framework for clustering is proposed
over specific partial algebraic systems by the present author. Her theory helps
in isolating minimal assumptions necessary for different concepts of clustering
information in any form to be realized in a situation (and therefore in a
semantics). \emph{It is well-known that of the limited number of proofs in the
theory of hard and soft clustering that are known to exist, most involve
statistical assumptions}. Many methods seem to work because they seem to work
in specific empirical practice. A new general rough method of analyzing
clusterings is invented, and this opens the subject to clearer conceptions and
contamination-free theoretical proofs. Numeric ideas of validation are also
proposed to be replaced by those based on general rough approximation. The
essence of the approach is explained in brief and supported by an example.
