  This paper examines the structure of poset matrices by formulating a set of
new construction rules for this purpose. In this direction, the technique of
partial composition operation will be introduced as the basis for the
construction of poset matrices of any given size by extending the combinatorial
setting of species of structures to poset matrices. More specifically, three
new partial composition operations that apply to poset matrices are defined as
the foundation for this study. Several new structural properties derived from
viewing any poset matrix and its dual in terms of these operations are
highlighted.
