1. A lattice database management system comprising: a computer including a lattice data set and a mechanism to identify a subset of lattice data elements associated with a particular concept from the lattice data set; wherein the lattice data set comprises: A. a plurality of data elements, each of which is associated with a concept from a set of concepts having a partial order structure, wherein that set is hereinafter referred to as a partial order of concepts (POC), B. a plurality of paths between one or more data elements associated with a concept and one or more other data elements associated with another concept, the plurality of paths defining a relationship between data elements in accord with the partial order of the concepts with which the data elements are associated, such that: (i) when data element a is associated with concept A, data element b is associated with concept B, and there is a path (a, b) between a and b, A<B in the partial order of concepts, and (ii) when there exists a path from a first data element associated with a first concept to a second data element associated with a second concept, all paths from the first data element to the second concept terminate on the second data element, C. wherein the lattice data set is referred to hereinafter as a lattice data set with a partial order of concepts (LDSWPOC); and D. wherein the plurality of paths define a relationship between data elements in the lattice data set such that: (iii) for data elements a, b, c, when: a is associated with concept A, b is associated with concept B, c is associated with concept C, there exists a path (a, b) from a to b; there exists a path (a, c) from a to c; and the inequality B<C is defined in the partial order of concepts, there exists a path (b, c) from b to c.