A Binary Matrix Model is a binary matrix and three associations (indicated by colons), i.e.
M = { N, V: Is, H: It, R̂: R }
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N: abinarymatrix V: a set of contextual elements associated in a one-to-one manner with the vertical index set Is of N, H is a set of contextual elements associated in a one-to-one manner with the horizontal index set I, of N
I: a contextual relation associated with the binary relation induced on I,xI,byN.
ThesetVis called the vertical index set of the model, and H is its horizontal index set.
The contextual relation I is called the model relation, and the matrix N is called the model matrix. Also, N may often be given a specific name for a specific kind of binary-matrix model.