Search results
Results From The WOW.Com Content Network
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 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 .
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.
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.
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 ]
A fundamental structure in mathematics and logic that consists of two elements arranged in a specific order, typically represented as (a, b). ostensive definition A definition that explains the meaning of a term or symbol by pointing to examples and counterexamples of the concept it represents.
The "up" in "climb up" is not always redundant, as in the example "He climbed up and then fell down the mountain." Many other examples of pleonasm are redundant only if the speaker's knowledge is taken into account. For example, most English speakers would agree that "tuna fish" is redundant because tuna is a kind of fish.