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In first-order logic, resolution condenses the traditional syllogisms of logical inference down to a single rule. To understand how resolution works, consider the following example syllogism of term logic: All Greeks are Europeans. Homer is a Greek. Therefore, Homer is a European. Or, more generally: .
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The resolution step leads to a worst-case exponential blow-up in the size of the formula. The Davis–Putnam–Logemann–Loveland algorithm is a 1962 refinement of the propositional satisfiability step of the Davis–Putnam procedure which requires only a linear amount of memory in the worst case.
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Resolution calculi that include subsumption can model rule one by subsumption and rule two by a unit resolution step, followed by subsumption. Unit propagation, applied repeatedly as new unit clauses are generated, is a complete satisfiability algorithm for sets of propositional Horn clauses ; it also generates a minimal model for the set if ...
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