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The resolution rule, as defined by Robinson, also incorporated factoring, which unifies two literals in the same clause, before or during the application of resolution as defined above. The resulting inference rule is refutation-complete, [ 6 ] in that a set of clauses is unsatisfiable if and only if there exists a derivation of the empty ...
A graphical representation of a partially built propositional tableau. In proof theory, the semantic tableau [1] (/ t æ ˈ b l oʊ, ˈ t æ b l oʊ /; plural: tableaux), also called an analytic tableau, [2] truth tree, [1] or simply tree, [2] is a decision procedure for sentential and related logics, and a proof procedure for formulae of first-order logic. [1]
The name "SLD resolution" was given by Maarten van Emden for the unnamed inference rule introduced by Robert Kowalski. [1] Its name is derived from SL resolution, [2] which is both sound and refutation complete for the unrestricted clausal form of logic. "SLD" stands for "SL resolution with Definite clauses".
Proof by contradiction is similar to refutation by contradiction, [4] [5] also known as proof of negation, which states that ¬P is proved as follows: The proposition to be proved is ¬P . Assume P .
It was introduced in 1961 by Martin Davis, George Logemann and Donald W. Loveland and is a refinement of the earlier Davis–Putnam algorithm, which is a resolution-based procedure developed by Davis and Hilary Putnam in 1960. Especially in older publications, the Davis–Logemann–Loveland algorithm is often referred to as the "Davis–Putnam ...
A (resolution) refutation of C is a resolution proof of from C. It is a common given a node η {\displaystyle \eta } , to refer to the clause η {\displaystyle \eta } or η {\displaystyle \eta } ’s clause meaning the conclusion clause of η {\displaystyle \eta } , and (sub)proof η {\displaystyle \eta } meaning the (sub)proof having η ...
Logically, the Prolog engine tries to find a resolution refutation of the negated query. The resolution method used by Prolog is called SLD resolution . If the negated query can be refuted, it follows that the query, with the appropriate variable bindings in place, is a logical consequence of the program.
Otter, developed at the Argonne National Laboratory, is based on first-order resolution and paramodulation. Otter has since been replaced by Prover9 , which is paired with Mace4 . SETHEO is a high-performance system based on the goal-directed model elimination calculus, originally developed by a team under direction of Wolfgang Bibel .