Pattern Recognition on Oriented Matroids

1.5Selected Mathematical Concepts and Tools for an Analysis of Infeasible Systems of Constraints

In this section we survey several mathematical concepts and tools discussed in Chapters 2-6, which can be useful in an analysis of infeasible systems of constraints.

Recall that an infeasible monotone system is defined to be a finite nonempty collection ${\mathbb{S}}^{r(M)-1}$ of constraints, together with a map π : (m) 2Γ from the Boolean lattice B(m) of subsets of the index set [m] to the power set of a nonempty set Γ (that is, to the unordered family of all subsets of Γ) such that

$\begin{array}{l}\pi \left(\stackrel{⌢}{0}\right)\cancel{=}\cancel{0};\\ \end{array}$