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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.
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.
The LRES rule resembles the resolution rule for classical propositional logic, where any propositional literals and are eliminated: ′ ′. The LERES rule states that if two propositional names p {\displaystyle p} and p ′ {\displaystyle p'} are equivalent, then p {\displaystyle \Box p} and ¬ p ′ {\displaystyle \neg \Box p'} can be eliminated.
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