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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] Like pleonasm, tautology is often considered a fault of style when
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 may refer to: Tautology (language), a redundant statement in literature and rhetoric; Tautology (logic), in formal logic, a statement that is true in every ...
Syntactic proof systems, in contrast, focus on the formal manipulation of symbols according to specific rules. The notion of syntactic consequence, φ ⊢ ψ {\displaystyle \varphi \vdash \psi } , signifies that ψ {\displaystyle \psi } can be derived from φ {\displaystyle \varphi } using the rules of the formal system.
The words need not be etymologically related, but simply conceptually, to be considered an example of cognate object: "We wept tears of joy." Such constructions are not actually redundant (unlike "She slept a sleep" or "We wept tears") because the object's modifiers provide additional information.
A term that describes itself. For example, the word "short" is autological because it is a short word. automaton A self-operating machine or, in computer science, a theoretical model of computation that performs tasks according to a set of rules or a program. automorphism
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.