Style Formula Resolution For Free

Resolution is a proof technique that works on conjunctive normal form expressions by (1) selecting two clauses that contain conflicting terms, (2) combining the terms contained in those two clauses, and then (3) canceling the terms that conflict.

The resolution rule is applied to all possible pairs of clauses that contain complementary literals. After each application of the resolution rule, the resulting sentence is simplified by removing repeated literals. If the clause contains complementary literals, it is discarded (as a tautology).

The resolution principle, due to Robinson (1965), is a method of theorem proving that proceeds by constructing refutation proofs, i.e., proofs by contradiction. This method has been exploited in many automatic theorem provers. The resolution principle applies to first-order logic formulas in Skolemized form.

In mathematical logic and automated theorem proving, resolution is a rule of inference leading to a refutation complete theorem-proving technique for sentences in propositional logic and first-order logic.

Resolution method is an inference rule which is used in both Propositional as well as First-order Predicate Logic in different ways. This method is basically used for proving the satisfiability of a sentence. In resolution method, we use Proof by Refutation technique to prove the given statement.

Resolution rules are a set of criteria that the system uses to define how compared entities resolve (if they are or are not the same entity) and relate (if entities are not resolved to the same entity, how many attributes they share).

The resolution principle, introduced by Robinson (1965), is a generalization of modus ponens and arose in the area of automated theorem proving where it was used to prove that a theorem can be derived from a set of axioms. This approach underpins the logic programming and production rules paradigms.

Resolution rule is simply a "generalization" of modus ponens : "from p?q and p, derive q". In classical logic, you can rewrite p?q as ¬p?q.