The link grammar dictionary consists of a collection of entries, each of which defines the linking requirements of one or more words. These requirements are specified by means of a formula of connectors combined by the binary associative operators =13& and =13or. Presidence is specified by means of parentheses. Without loss of generality we may assume that a connector is simply a character string ending in + or -.
When a link connects to a word, it is associated with one of the connectors of the formula of that word, and it is said to satisfy that connector. No two links may satisfy the same connector. The connectors at opposite ends of a link must have names that match, and the one on the left must end in + and the one on the right must end in -. In basic link grammars, two connectors match if and only if their strings are the same (up to but not including the final + or -). A more general form of matching will be introduced later.
The connectors satisfied by the links must serve to satisfy the whole formula. We define the notion of satisfying a formula recursively. To satisfy the =13& of two formulas, both formulas must be satisfied. To satisfy the =13or of two formulas, one of the formulas must be satisfied, and no connectors of the other formula may be satisfied. It is sometimes convenient to use the empty formula (``()''), which is satisfied by being connected to no links.
A sequence of words is a sentence of the language defined by the grammar if there exists a way to draw links among the words so as to satisfy each word's formula, and the following meta-rules: