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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 ...
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 .
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.
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 cut-elimination theorem (or Gentzen's Hauptsatz) is the central result establishing the significance of the sequent calculus.It was originally proved by Gerhard Gentzen in his landmark 1934 paper "Investigations in Logical Deduction" for the systems LJ and LK formalising intuitionistic and classical logic respectively.
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Resolution (logic), a rule of inference used for automated theorem proving Standard resolution , the bar construction of resolutions in homological algebra Resolution of singularities in algebraic geometry