A half cadence (HC) occurs when a phrase ends with a (root-position) dominant triad. A phrase that ends with a HC requires continuation; it is analogous to a comma or semicolon in the middle of a sentence.
• Sometimes the root-position dominant triad that forms the usual goal of a phrase ending in a half cadence will be replaced by an inverted dominant triad, dominant seventh, or inverted dominant seventh. This is less common prior to Beethoven, but becomes increasingly common in the music of nineteenth-century composers.
• What if the cadential dominant is preceded not by some diatonic chord but by its own applied dominant -- is the cadence is a half cadence in the tonic key, or an authentic cadence in the key of the dominant, or even in some sense both at once? Here context helps us. If after such a "three-quarter half cadence" the music continues in the tonic key, we may assume that the applied dominant was of mainly ornamental significance. if, on the other hand, the music resumes in the dominant key, we will retrospectively hear the "three-quarter cadence" as the start of a tonicization of V.