Chaining, unit propagation, and resolution. Recall that the unit propagation inference rule is: given KB containing clauses C_1; : : : ;C_k and a partial assignment if some C_ij consists of a single literal L, add x_i = b such that L(b) = 1 to . Note that any x_2 element {0; 1}^n satisfying KB that is consistent with p must also have x_i = b. Unit propagation is a particularly ecient inference rule used by SAT-solvers.

(a) Show that if there is a (forward) chaining derivation of a literal L from KB (and not of "not" L), then repeated application of unit propagation starting from the empty partial assignment (* : : : *) applied to KB eventually obtains a partial assignment that satises

L. (That is, "unit propagation simulates chaining.")

Chaining, unit propagation, and resolution. Recall that the unit propagation infer- ence rule is: given KB containing clauses C1, . . . , Ck and a partial assignment if some Cil consists of a single literal 1, add ri = b such that 1(b) = 1 to . Note that any 1 e {0, 1)" sat- isfying KB that is consistent with must also have zi-. Unit propagation is a particularly efficient inference rule used by SAT-solvers. (a) Show that if there is a (forward) chaining derivation of a literal from KB (and not of -l), then repeated application of unit propagation starting from the empty partial assignment (5- *) applied to KB eventually obtains a partial assignment that satisfies . (That is, "unit propagation simulates chaining.") Chaining, unit propagation, and resolution. Recall that the unit propagation infer- ence rule is: given KB containing clauses C1, . . . , Ck and a partial assignment if some Cil consists of a single literal 1, add ri = b such that 1(b) = 1 to . Note that any 1 e {0, 1)" sat- isfying KB that is consistent with must also have zi-. Unit propagation is a particularly efficient inference rule used by SAT-solvers. (a) Show that if there is a (forward) chaining derivation of a literal from KB (and not of -l), then repeated application of unit propagation starting from the empty partial assignment (5- *) applied to KB eventually obtains a partial assignment that satisfies . (That is, "unit propagation simulates chaining.")