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tautology
tautology (tɔːˈtɒlədʒɪ) [ad. late L. tautologia (c 350 in Mar. Plotin. Sacerd.), a. Gr. ταὐτολογία, f. ταὐτολόγος: see tautologous; in F. tautologie.] a. A repetition of the same statement. b. The repetition (esp. in the immediate context) of the same word or phrase, or of the same idea or statement... Oxford English Dictionary
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Tautology
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 See also Pleonasm Redundancy (disambiguation wikipedia.org
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grammaticality - Tautology: extensive periods of time - English ...
Tautology is: the saying of the same thing twice over in different words, generally considered to be a fault of style ( e.g. they arrived one after the other in succession ). ODO, via Google. It is important to understand that a period of time can be any length, and your premise that 'a period of time' repeats the meaning of extensive is incorrect.
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tautology
tautology/tɔ:ˈtɔlədʒɪ; tɔ`tɑlədʒɪ/ n(a) [U] saying the same thing more than once in different ways withoutmaking one's meaning clearer or more forceful; needlessrepetition 无谓的重复; 赘述.(b) [C] instance of this 重复的话; 赘言. Cf 参看 pleonasm. 牛津英汉双解词典
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Tautology (logic) - Wikipedia
Tautology (logic) In mathematical logic, a tautology (from Greek: ταυτολογία) is a formula or assertion that is true in every possible interpretation. An example is "x=y or x≠y". Similarly, "either the ball is green, or the ball is not green" is always true, regardless of the colour of the ball. The philosopher Ludwig Wittgenstein ...
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Tautology (logic)
A minimal tautology is a tautology that is not the instance of a shorter tautology. For example, because is a tautology of propositional logic, is a tautology in first order logic. wikipedia.org
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Is A∨¬A a tautology when there is a proof (by contradiction)? $A \lor \neg A$ is stated as a "tautology", but is it really a tautology? It can be proven by counterposition. And therefore it is not a tautology when it ...
$A\vee \neg A$ is a tautology in classical (i.e., Aristotelian) logic because you can prove that using the deduction rules of the classical proposition That is the meaning of tautology. In non-classical logical systems, such as intuitionism or constructivism, $A \vee \neg A$ is not a tautology.
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Tautology (rule of inference)
In propositional logic, tautology is either of two commonly used rules of replacement. The tautology rule may be expressed as a sequent: and where is a metalogical symbol meaning that is a syntactic consequence of , in the one case wikipedia.org
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Prove this is a tautology with logical equivalence laws only. $[(p \lor q) \land (\lnot p \lor r)] \to (q \lor r)$ is a tautology I'm not sure how to prove this is a tautology. Tried using $(p \to q)\equiv (\lnot p \l...
\tag{*} $$ (Every instance of $[(A\to B)\land(B\to C)]\to (A\to C)$ is a tautology, a theorem, is valid; so from that together with (Hyp.), (*) follows
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Tautology (language)
a logical tautology always is. See also References External links Figures of Speech: Tautology Tautology Explained Sentences by type Rhetoric Linguistics Propositions Semantics wikipedia.org
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Prove that if $\alpha$ is a tautology then $subst(\alpha,s)$ is a tautology > Prove that if $\alpha$ is a tautology then $subst(\alpha,s)$ is a tautology for every $s\in WFF^{Var}$ I know how to do this if $\alpha =\...
Consider now a tautology $\alpha$; we have that $v \vDash \alpha$, for every valuation $v$. But this holds for every valuation $v$, and thus $\alpha^s$ is a tautology.
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condition for a CNF formula to be a tautology Is there an easy condition (for example based on clauses) that implies that a formula in CNF is a tautology? Or is this as hard as for general formulas (not in CNF)? I fi...
Such a statement is a tautology if and only if each and every clause is a tautology. A clause is a tautology if and only if either (1) one of the literals is a true valued constant or (2) the clause contains both a literal and its own negation
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Is the proposition $\forall x: P(x)$ a tautology? If $P(x)$ is a predicate and for all x: $P(x)$ is true, does that make the proposition $(\forall x: P(x))$ a tautology? Or is it not a tautology because P(x) can be d...
Putting it crudely, a necessary condition for a sentence counting as a tautology is that it is true as a matter of logic alone (some would require more If $P$ means "is male", and the domain is Presidents of the US, past and present, then $\forall xPx$ is true: but that's not a tautology on any account
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Tautology And Substitution Let $ \alpha $ be some proposition, and let $ A = \alpha $, and let $ B = \neg \alpha $. Is the statement $ A \lor B $ a tautology?
Obviously, $α ∨ ¬α$ is a _tautology_. But - in general - $A∨B$ is not a tautology. The "rule" is: > every _instance_ of a _tautological schema_ will be a tautology.
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How is negation of a tautology a tautology? I am reading the book Elements of Discrete Mathematics by C L Liu. On the first chapter about Sets and Propositions, under the heading TAUTOLOGIES the author states > It ma...
The negation of a tautology#Definition_and_examples) is a formula that is Always FALSE, i.e. a contradiction. * * * _Note_ added June 27.
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