 It is also important to note that, in dependence logic, disjunction is not idempotent: for example, \(\eqord(x,y) \lor \eqord(x,y)\) is not equivalent to \(\eqord(x,y)\), and it is satisfied by a team \(X\) if and only if for every three assignments in \(X\) which agree on \(x\) at least two agree on \(y\). This may appear somewhat counter-intuitive; but it is a straightforward consequence of the fact that, under our interpretation, \(\eqord(x,y) \lor \eqord(x,y)\) is to be read as “every possible state of things comes from one of two sets of states of things, and in both of them \(y\) is a function of \(x\)”. Since the union of functions is not in general a function, it comes to little surprise that disjunction in dependence logic is not idempotent.