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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.
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 .
Each logic operator can be used in an assertion about variables and operations, showing a basic rule of inference. Examples: The column-14 operator (OR), shows Addition rule: when p=T (the hypothesis selects the first two lines of the table), we see (at column-14) that p∨q=T.
In fact, the resolution of a goal clause with a definite clause to produce a new goal clause is the basis of the SLD resolution inference rule, used in implementation of the logic programming language Prolog. In logic programming, a definite clause behaves as a goal-reduction procedure.
The resolution rule is a single rule of inference that, together with unification, is sound and complete for first-order logic. As with the tableaux method, a formula is proved by showing that the negation of the formula is unsatisfiable. Resolution is commonly used in automated theorem proving.
In proof theory, an area of mathematical logic, resolution proof reduction via local context rewriting is a technique for resolution proof reduction via local context rewriting. [1] This proof compression method was presented as an algorithm named ReduceAndReconstruct , that operates as a post-processing of resolution proofs.
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Backward chaining is implemented in logic programming by SLD resolution. Both rules are based on the modus ponens inference rule. It is one of the two most commonly used methods of reasoning with inference rules and logical implications – the other is forward chaining. Backward chaining systems usually employ a depth-first search strategy, e ...