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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. They are: The principle of idempotency of disjunction:
A set of rules can be used to infer any valid conclusion if it is complete, while never inferring an invalid conclusion, if it is sound. A sound and complete set of rules need not include every rule in the following list, as many of the rules are redundant, and can be proven with the other rules.
Many logicians in the early 20th century used the term 'tautology' for any formula that is universally valid, whether a formula of propositional logic or of predicate logic. In this broad sense, a tautology is a formula that is true under all interpretations, or that is logically equivalent to the negation of a contradiction.
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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 ]
'''bold''' ''italics'' <sup>superscript</sup> <sub>superscript</sub> → bold: → italics: → superscript → subscript <s>strikeout</s> <u>underline</u> <big>big ...
Transformation rules; Propositional calculus; Rules of inference; Implication introduction / elimination (modus ponens) Biconditional introduction / elimination; Conjunction introduction / elimination; Disjunction introduction / elimination; Disjunctive / hypothetical syllogism; Constructive / destructive dilemma
[2] [5] The internal lexicon encompasses every learned word, even exception words like 'colonel' or 'pint' that don't follow letter-to-sound rules. This route doesn't enable reading of nonwords (e.g. 'zuce'), though some phonological output can still be produced by matching the word to an approximation in the lexicon (e.g. 'sare' activating ...