The head or headword of a phrase is the most important word in a phrase. It determines the syntactic category of the phrase it heads: the head of an NP is a noun; the head of VP is a verb; the head of an AdjP is an adjective, the head of a PrepP is a preposition and the head of an AdvP is an adverb. (AEG Ch. 1)
Headword, see head
Hypothetical Clause
A hypothetical clause is a clause that represents a situation as hypothetical. In AEG, the term hypothetical clause is used to refer to if-clauses that represent a present or future situation as possible: If it rains tomorrow, we'll cancel the match; If I caught a student cheating, the sanctions would be severe. (AEG Ch4; Ch5)