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In propositional logic, tautology is either of two commonly used rules of replacement. [ 1 ] [ 2 ] [ 3 ] The rules are used to eliminate redundancy in disjunctions and conjunctions when they occur in logical proofs .
Tautology; Predicate logic; ... Rules of inference are syntactical transform rules which one can use to infer a conclusion from a premise to create an argument. A set ...
Many logicians in the early 20th century used the term 'tautology' for any formula that is universally valid, whether a formula of propositional logic or of predicate logic. In this broad sense, a tautology is a formula that is true under all interpretations, or that is logically equivalent to the negation of a contradiction.
Tautology; Predicate logic; ... a rule of inference, inference rule or transformation rule is a logical form consisting of a function which takes premises, ...
where the rule is that wherever an instance of "()" appears on a line of a proof, it can be replaced with "()", and vice versa. Import-export is a name given to the statement as a theorem or truth-functional tautology of propositional logic:
Absorption is a valid argument form and rule of inference of propositional logic. [1] [2] The rule states that if implies , then implies and .The rule makes it possible to introduce conjunctions to proofs.
Tautology may refer to: Tautology (language), a redundant statement in literature and rhetoric; Tautology (logic), in formal logic, a statement that is true in every possible interpretation; Tautology (rule of inference), a rule of replacement for logical expressions
A propositional formula is a tautology if it is true under every valuation (or interpretation) of its predicate symbols. If Φ is a tautology, and Θ is a substitution instance of Φ, then Θ is again a tautology. This fact implies the soundness of the deduction rule described in the previous section.