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  2. Tautology (logic) - Wikipedia

    en.wikipedia.org/wiki/Tautology_(logic)

    The definition of tautology can be extended to sentences in predicate logic, which may contain quantifiers—a feature absent from sentences of propositional logic. Indeed, in propositional logic, there is no distinction between a tautology and a logically valid formula. In the context of predicate logic, many authors define a tautology to be a ...

  3. List of logic symbols - Wikipedia

    en.wikipedia.org/wiki/List_of_logic_symbols

    The following table lists many common symbols, together with their name, how they should be read out loud, and the related field of mathematics. Additionally, the subsequent columns contains an informal explanation, a short example, the Unicode location, the name for use in HTML documents, [ 1 ] and the LaTeX symbol.

  4. If and only if - Wikipedia

    en.wikipedia.org/wiki/If_and_only_if

    Wherever logic is applied, especially in mathematical discussions, it has the same meaning as above: it is an abbreviation for if and only if, indicating that one statement is both necessary and sufficient for the other. This is an example of mathematical jargon (although, as noted above, if is more often used than iff in statements of definition).

  5. Logical truth - Wikipedia

    en.wikipedia.org/wiki/Logical_truth

    However, the term tautology is also commonly used to refer to what could more specifically be called truth-functional tautologies. Whereas a tautology or logical truth is true solely because of the logical terms it contains in general (e.g. " every ", " some ", and "is"), a truth-functional tautology is true because of the logical terms it ...

  6. Vacuous truth - Wikipedia

    en.wikipedia.org/wiki/Vacuous_truth

    These examples, one from mathematics and one from natural language, illustrate the concept of vacuous truths: "For any integer x, if x > 5 then x > 3." [11] – This statement is true non-vacuously (since some integers are indeed greater than 5), but some of its implications are only vacuously true: for example, when x is the integer 2, the statement implies the vacuous truth that "if 2 > 5 ...

  7. Tautology - Wikipedia

    en.wikipedia.org/wiki/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 ...

  8. Tautology (rule of inference) - Wikipedia

    en.wikipedia.org/wiki/Tautology_(rule_of_inference)

    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 .

  9. Propositional proof system - Wikipedia

    en.wikipedia.org/wiki/Propositional_proof_system

    A propositional proof system P is polynomially bounded (also called super) if every tautology has a short (i.e., polynomial-size) P-proof. If P is polynomially bounded and Q simulates P, then Q is also polynomially bounded. The set of propositional tautologies, TAUT, is a coNP-complete set. A propositional proof system is a certificate-verifier ...