A
valuation function Σ⊆P(Cell)×N taking a
set of cells (often called a
neighborhood) to the number of bombs we know to be present between them. Note that the domain of
Σ is not necessarily all of
P(Cell), since we won’t know the
valuation of
all sets of cells (unless the game is
complete).
We could equivalently consider this
function to have signature
Σ:P(Cell)→{?}∪N, where
?∈/N denotes that the
valuation of a
neighborhood is unkown.