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  2. Sentence (mathematical logic) - Wikipedia

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

    Sentences are then built up out of atomic sentences by applying connectives and quantifiers. A set of sentences is called a theory; thus, individual sentences may be called theorems. To properly evaluate the truth (or falsehood) of a sentence, one must make reference to an interpretation of the theory.

  3. Frequentative - Wikipedia

    en.wikipedia.org/wiki/Frequentative

    Some frequentative verbs surviving in English, and their parent verbs are listed below. Additionally, some frequentative verbs are formed by reduplication of a monosyllable (e.g., coo-cooing, cf. Latin murmur). Frequentative nouns are often formed by combining two different vowel grades of the same word (as in teeter-totter, pitter-patter ...

  4. Statement (logic) - Wikipedia

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

    are two different sentences that make the same statement. In either case, a statement is viewed as a truth bearer. Examples of sentences that are (or make) true statements: "Socrates is a man." "A triangle has three sides." "Madrid is the capital of Spain." Examples of sentences that are also statements, even though they aren't true:

  5. Propositional calculus - Wikipedia

    en.wikipedia.org/wiki/Propositional_calculus

    Propositional logic deals with statements, which are defined as declarative sentences having truth value. [29] [1] Examples of statements might include: Wikipedia is a free online encyclopedia that anyone can edit. London is the capital of England. All Wikipedia editors speak at least three languages.

  6. Propositional formula - Wikipedia

    en.wikipedia.org/wiki/Propositional_formula

    For example, Hamilton uses two symbols = and ≠ when he defines the notion of a valuation v of any well-formed formulas (wffs) A and B in his "formal statement calculus" L. A valuation v is a function from the wffs of his system L to the range (output) { T, F }, given that each variable p 1 , p 2 , p 3 in a wff is assigned an arbitrary truth ...

  7. 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. The sentence may contain several such ...

  8. First-order logic - Wikipedia

    en.wikipedia.org/wiki/First-order_logic

    In this example, both sentences happen to have the common form () for some individual , in the first sentence the value of the variable x is "Socrates", and in the second sentence it is "Plato". Due to the ability to speak about non-logical individuals along with the original logical connectives, first-order logic includes propositional logic.

  9. Necessity and sufficiency - Wikipedia

    en.wikipedia.org/wiki/Necessity_and_sufficiency

    In logic and mathematics, necessity and sufficiency are terms used to describe a conditional or implicational relationship between two statements. For example, in the conditional statement: "If P then Q", Q is necessary for P, because the truth of Q is guaranteed by the truth of P.