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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.
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.
1 function ReduceAndReconstructLoop(/* a proof */): 2 TS = TopologicalSorting(); 3 for each node in TS 4 if is not a leaf 5 if and ¯ then 6 = Resolution(, ); 7 Determine left context of , if any; 8 Determine right context of , if any; 9 Heuristically choose one context (if any) and apply the corresponding rule; 10 else if and ¯ then 11 ...
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.
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 .
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This is the modus ponens rule of propositional logic. Rules of inference are often formulated as schemata employing metavariables. [2] In the rule (schema) above, the metavariables A and B can be instantiated to any element of the universe (or sometimes, by convention, a restricted subset such as propositions) to form an infinite set of ...