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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 (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 ...
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 Otter has since been replaced by Prover9 , which is paired with Mace4 .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 .
Prolog is a logic programming language that has its origins in artificial intelligence, automated theorem proving and computational linguistics. [1] [2] [3]Prolog has its roots in first-order logic, a formal logic, and unlike many other programming languages, Prolog is intended primarily as a declarative programming language: the program is a set of facts and rules, which define relations.
SLD 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 .
Vectorization first creates a resolution-independent vector representation of the graphic to be scaled. Then the resolution-independent version is rendered as a raster image at the desired resolution. This technique is used by Adobe Illustrator Live Trace, Inkscape, and several recent papers. [6]
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. Derive falsehood. Conclude ¬P. In contrast, proof by contradiction proceeds as follows: The proposition to be proved is P. Assume ¬P. Derive ...
A classic example of a production rule-based system is the domain-specific expert system that uses rules to make deductions or choices. [1] For example, an expert system might help a doctor choose the correct diagnosis based on a cluster of symptoms, or select tactical moves to play a game.