To clarify further, let us introduce the distinction between contradictories and opposites. The PNC is concerned with the former. However, it has an ancestor in a famous passage of Plato’s Republic, which is concerned with opposites.
Principle of Opposites: The same thing will not be willing to do or undergo opposites in the same part of itself, in relation to the same thing, at the same time. (Plato, Republic 436b)
For example, cold and hot, tall and small, odd and even, are opposites.
Contradictories, however, are strictly each other’s negation, for example, cold and not-cold, tall and not-tall, and so on. In terms of the semantic version, this can also be formulated as follows: the proposition “X is cold” and “It is not the case that X is cold” are contradictories. Likewise, “X is cold” and “X is not-cold” are contradictories, unless it is further specified that X is cold in some sense, but not another, or that X is cold at some time/place, but not at another.