Inverse Resolution

Definition

Inverse resolution is, as the name indicates, a rule that inverts resolution. This follows the idea of induction as the inverse of deduction formulated in the logic of generality. The resolution rule is the best-known deductive inference rule, used in many theorem provers and logic programming systems. Resolution starts from two clauses and derives the resolvent, a clause that is entailed by the two clauses. This can be graphically represented using the following schema (for propositional logic).

$$\displaystyle\begin{array}{rcl} \frac{h \leftarrow g,a_{1},\ldots,a_{n}\ \text{and}\ g \leftarrow b_{1},\ldots,b_{m}} {h \leftarrow b_{1},\ldots,b_{m},a_{1},\ldots,a_{n}} .& & {}\\ \end{array}$$

Inverse resolution operators, such as absorption (17) and identification (17), invert this process. To this aim, they typically assume the resolvent is given together with oneof the original clauses and then derive the missing clause. This leads to the following two operators, which...