A partial function on a space \(S\) is a function that assigns values to some, but not necessarily to all, members of \(S\). Said otherwise, it is a function whose domain is a subset of \(S\). For a partial function \(f\), \(f(x)\simeq y\) means \(x\) is in the domain of \(f\) and \(f(x) = y\). (Finally we have a proper accounting of our use of \(\simeq\) in the examples earlier.) Partial relations are partial functions from \(k\)-tuples to \(\{{\textsf{t}}, {\textsf{f}}\}\). The given relations of our structures are relations in the usual sense, but it is partial relations that we may find ourselves defining.