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The resolution rule in propositional logic is a single valid inference rule that produces a new clause implied by two clauses containing complementary literals. A literal is a propositional variable or the negation of a propositional variable.
we express our hypotheses and conclusion as a product of sums (conjunctive normal form), such as those that appear in the Resolution Tautology. Each max term in the CNF of the hypothesis becomes a clause in the proof.
In mathematical logic and automated theorem proving, resolution is a rule of inference leading to a refutation theorem-proving technique for sentences in propositional logic and first-order logic. The clause produced by a resolution rule is sometimes called a resolvent.
Resolution Principle. 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 proves.
The Relational Resolution Principle is analogous to that of propositional resolution. The main difference is the use of unification to unify literals before applying the rule.
Push negations into the formula, repeatedly applying De Morgan's Law, until all negations only apply to atoms. You obtain a formula in negation normal form. Repeatedly apply the distributive law where a disjunction occurs over a conjunction. Once this is not possible anymore, the formula is in CNF.
OLD resolution (Selective Linear Definite clause resolution) is the basic inference rule used in logic programming. It is a refinement of resolution, which is both sound and refutation complete for Horn clauses.
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