propositional function

propositional function

* * *

Sentencelike expression that may be thought of as obtained from a sentence by substituting variables for constants occurring in the sentence.

For example, "x was a parent of y" may be thought of as obtained from "Adam was a parent of Abel." A propositional function therefore has no truth-value, becoming true or false only when its free variables are replaced by constants of appropriate syntactic categories (e.g., "Abraham was a parent of Isaac").

* * *

      in logic, a statement expressed in a form that would take on a value of true or false were it not for the appearance within it of a variable x (or of several variables), which leaves the statement undetermined as long as no definite values are specified for the variables. Denoted as a mathematical function, A(x) or A(x1, x2, · · ·, xn), the propositional function is an abstraction from propositional forms (or predicates). For example, “x is small,” “x ist klein,” and “x is not large” are all propositional forms. The substitution of some noun (or value) for x yields a specific proposition that is either true or false, but “x is small” itself has no truth-value. Abstracting from these three propositional forms yields a propositional function A(x), which has, for example, the value true when x takes the value mouse and has the value false when x is elephant.

      Propositional functions permit the treatment in symbolic logic of propositions the truth of which is contingent upon variable components.

* * *

Universalium. 2010.

Игры ⚽ Поможем решить контрольную работу

Look at other dictionaries:

  • propositional function — n. Logic an expression containing at least one variable, that becomes a proposition when a constant is substituted for the variable (Ex.: x is a man) …   English World dictionary

  • propositional function — The concept introduced by Frege of a function taking a number of names as arguments, and delivering one proposition as the value. The idea is that ‘ x loves y ’ is a propositional function, which yields the proposition ‘John loves Mary’ for those …   Philosophy dictionary

  • propositional function — noun 1. : sentential function 2. : something that is designated or expressed by a sentential function * * * Logic. See sentential function. [1900 05] * * * propositional function, 1. a combination of two or more propositions whose truth or… …   Useful english dictionary

  • propositional function — noun Date: 1903 1. sentential function 2. something that is designated or expressed by a sentential function …   New Collegiate Dictionary

  • propositional function — proposi′tional func′tion n. pho sentential function • Etymology: 1900–05 …   From formal English to slang

  • propositional function — noun An expression containing algebraic symbols that serve to represent words or other elements of a sentence or proposition …   Wiktionary

  • Function (mathematics) — f(x) redirects here. For the band, see f(x) (band). Graph of example function, In mathematics, a function associates one quantity, the a …   Wikipedia

  • propositional — See proposition. * * * (as used in expressions) propositional attitude propositional calculus propositional function * * * …   Universalium

  • function — /fungk sheuhn/, n. 1. the kind of action or activity proper to a person, thing, or institution; the purpose for which something is designed or exists; role. 2. any ceremonious public or social gathering or occasion. 3. a factor related to or… …   Universalium

  • Propositional calculus — In mathematical logic, a propositional calculus or logic (also called sentential calculus or sentential logic) is a formal system in which formulas of a formal language may be interpreted as representing propositions. A system of inference rules… …   Wikipedia

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”