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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 mathematical logic, a tautology (from Ancient Greek: ταυτολογία) is a formula that is true regardless of the interpretation of its component terms, with only the logical constants having a fixed meaning.
where is a metalogical symbol meaning that is a syntactic consequence of , in the one case, in the other, in some logical system; or as a rule of inference : P ∨ P ∴ P {\displaystyle {\frac {P\lor P}{\therefore P}}}
In mathematics, tautological may refer to: Logic: Tautological consequence; Geometry, where it is used as an alternative to canonical: Tautological bundle; Tautological line bundle; Tautological one-form; Tautology (grammar), unnecessary repetition, or more words than necessary, to say the same thing.
The following is a list of place names often used tautologically, plus the languages from which the non-English name elements have come. Tautological place names are systematically generated in languages such as English and Russian, where the type of the feature is systematically added to a name regardless of whether it contains it already.
The accounts discussed above all yield monotonic consequence relations, i.e. ones such that if is a consequence of , then is a consequence of any superset of . It is also possible to specify non-monotonic consequence relations to capture the idea that, e.g., 'Tweety can fly' is a logical consequence of
A bilingual tautological expression is a phrase that combines words that mean the same thing in two different languages. [8]: 138 An example of a bilingual tautological expression is the Yiddish expression מים אחרונים וואַסער mayim akhroynem vaser. It literally means "water last water" and refers to "water for washing the ...
"Convicted felon", a common English phrase. All felons are convicted by the definition of felon. "Only time will tell if we stand the test of time", from the Van Halen song "Why Can't This Be Love" "After we change the game it won't remain the same." from the Blackalicious song "Blazing Arrow" "That tautological statement has repeated an idea."