A correspondent writes to ask about the difference between 'complete' and 'incomplete' predication, which she and her colleagues have found confusing.
I'm not surprised. It's not a pair of terms I come across much these days. Terms based on 'completeness' are more associated with Victorian grammars, and they rather fell into disrepute when structural linguistics developed. But the underlying concept is still an important part of any modern grammar, even though analyses vary somewhat.
A verb which can stand alone as a predicate (i.e. without any complementation) would be a 'complete' predicate, in these terms. It's gone, I complained, and so on.
An 'incomplete' predicate would be a verb which requires some sort of complementation for the sentence to be grammatical. In the terms I like to use, this would be an object (a transitive verb, e.g. I saw a dog), an adverbial (e.g. They kept out of trouble) or a complement (in a narrow sense, e.g. I am ready).
Notice that the class a verb belongs to depends on its meaning: I kept a cat is different from I kept out of trouble. Similarly, we need to distinguish between I'm eating and I'm eating a cake. In other words, we're talking here about different uses of verbs - a more helpful way of thinking, to my mind, than to set up an absolute contrast, such as is implied by 'complete' vs 'incomplete'.
A Comprehensive Grammar of the English Language (§§16.20ff) has an excellent listing of verbs in different complementation functions.