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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.
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.
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 .
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 ...
Starting from these eight tautologies and a tacit use of the "rule" of substitution, PM then derives over a hundred different formulas, among which are the Law of Excluded Middle 1.71, and the Law of Contradiction 3.24 (this latter requiring a definition of logical AND symbolized by the modern ⋀: (p ⋀ q) = def ~(~p ⋁ ~q).
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
Law of logic may refer to: Basic laws of Propositional Logic or First Order Predicate Logic; Laws of thought, which present first principles (arguably) before reasoning begins; Rules of inference, which dictate the valid use of inferential reasoning
Logic is the formal science of using reason and is considered a branch of both philosophy and mathematics and to a lesser extent computer science. Logic investigates and classifies the structure of statements and arguments, both through the study of formal systems of inference and the study of arguments in natural language .