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  2. Sentence (mathematical logic) - Wikipedia

    en.wikipedia.org/wiki/Sentence_(mathematical_logic)

    In mathematical logic, a sentence (or closed formula) [1] of a predicate logic is a Boolean-valued well-formed formula with no free variables. A sentence can be viewed as expressing a proposition , something that must be true or false.

  3. Open formula - Wikipedia

    en.wikipedia.org/wiki/Open_formula

    An open formula is a formula that contains at least one free variable. [citation needed] An open formula does not have a truth value assigned to it, in contrast with a closed formula which constitutes a proposition and thus can have a truth value like true or false. An open formula can be transformed into a closed formula by applying a ...

  4. Propositional formula - Wikipedia

    en.wikipedia.org/wiki/Propositional_formula

    Evaluation of a propositional formula begins with assignment of a truth value to each variable. Because each variable represents a simple sentence, the truth values are being applied to the "truth" or "falsity" of these simple sentences. Truth values in rhetoric, philosophy and mathematics. The truth values are only two: { TRUTH "T", FALSITY "F" }.

  5. Well-formed formula - Wikipedia

    en.wikipedia.org/wiki/Well-formed_formula

    A closed formula, also ground formula or sentence, is a formula in which there are no free occurrences of any variable. If A is a formula of a first-order language in which the variables v 1, …, v n have free occurrences, then A preceded by ∀v 1 ⋯ ∀v n is a universal closure of A.

  6. First-order logic - Wikipedia

    en.wikipedia.org/wiki/First-order_logic

    Infinitely long sentences arise in areas of mathematics including topology and model theory. Infinitary logic generalizes first-order logic to allow formulas of infinite length. The most common way in which formulas can become infinite is through infinite conjunctions and disjunctions.

  7. 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.

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  9. Propositional function - Wikipedia

    en.wikipedia.org/wiki/Propositional_function

    In propositional calculus, a propositional function or a predicate is a sentence expressed in a way that would assume the value of true or false, except that within the sentence there is a variable (x) that is not defined or specified (thus being a free variable), which leaves the statement undetermined.

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