Unit Propagation - Definition

Definition

The procedure is based on unit clauses, i.e. clauses that are composed of a single literal. If a set of clauses contains the unit clause, the other clauses are simplified by the application of the two following rules:

1. every clause containing is removed;
2. in every clause that contains this literal is deleted.

The application of these two rules lead to a new set of clauses that is equivalent to the old one. For example, the following set of clauses can be simplified by unit propagation because it contains the unit clause .

Since contains the literal, this clause can be removed altogether. Since contains the negation of the literal in the unit clause, this literal can be removed from the clause. The unit clause is not removed; this would make the resulting set not equivalent to the original one; this clause can be removed if already stored in some other form (see section "Using a partial model"). The effect of unit propagation can be summarized as follows.

The resulting set of clauses is equivalent to the above one. The new unit clause that results from unit propagation can be used for a further application of unit propagation, which would transform into .