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For example, because is a tautology of propositional logic, ((=)) ((=)) is a tautology in first order logic. Similarly, in a first-order language with a unary relation symbols R,S,T, the following sentence is a tautology:
In literary criticism and rhetoric, a tautology is a statement that repeats an idea using near-synonymous morphemes, words or phrases, effectively "saying the same thing twice". [ 1 ] [ 2 ] Tautology and pleonasm are not consistently differentiated in literature. [ 3 ]
However, the term tautology is also commonly used to refer to what could more specifically be called truth-functional tautologies. Whereas a tautology or logical truth is true solely because of the logical terms it contains in general (e.g. " every ", " some ", and "is"), a truth-functional tautology is true because of the logical terms it ...
Tautological consequence can also be defined as ∧ ∧ ... ∧ → is a substitution instance of a tautology, with the same effect. [2]It follows from the definition that if a proposition p is a contradiction then p tautologically implies every proposition, because there is no truth valuation that causes p to be true and so the definition of tautological implication is trivially satisfied.
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 .
For example, consider the following English sentences: "I know you're coming." "I know that you're coming." In this construction, the conjunction that is optional when joining a sentence to a verb phrase with know. Both sentences are grammatically correct, but the word that is pleonastic in this case.
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 ...
Propositional logic, as currently studied in universities, is a specification of a standard of logical consequence in which only the meanings of propositional connectives are considered in evaluating the conditions for the truth of a sentence, or whether a sentence logically follows from some other sentence or group of sentences.