Resolution (logic)

Resolution (logic)

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. In other words, iteratively applying the resolution rule in a suitable way allows for telling whether a propositional formula is satisfiable and for proving that a first-order formula is unsatisfiable; this method may prove the satisfiability of a first-order satisfiable formula, but not always, as it is the case for all methods for first-order logic (see Gödel's incompleteness theorems and Halting problem). Resolution was introduced by John Alan Robinson in 1965.

The clause produced by a resolution rule is sometimes called a resolvent.