# Predicate logic

﻿
Predicate logic

In mathematical logic, predicate logic is the generic term for symbolic formal systems like first-order logic, second-order logic, many-sorted logic or infinitary logic. This formal system is distinguished from other systems in that its formulas contain variables which can be quantified. Two common quantifiers are the existential &exist; and universal &forall; quantifiers. The variables could be elements in the universe, or perhaps relations or functions over the universe. For instance, an existential quantifier over a function symbol would be interpreted as modifier "there is a function".

In informal usage, the term "predicate logic" occasionally refers to first-order logic. Some authors consider the predicate calculus to be an axiomatized form of predicate logic, and the predicate logic to be derived from an informal, more intuitive development. [Among these authors is Stolyar, p. 166. Hamilton considers both to be calculi but divides them into an informal calculus and a formal calculus.]

Footnotes

References

* A. G. Hamilton 1978, "Logic for Mathematicians", Cambridge University Press, Cambridge UK ISBN 0-521-21838-1.
*Abram Aronovic Stolyar 1970, "Introduction to Elementary Mathematical Logic", Dover Publications, Inc. NY. ISBN 0-486-64561

Wikimedia Foundation. 2010.

### Look at other dictionaries:

• Predicate (logic) — Sometimes it is inconvenient or impossible to describe a set by listing all of its elements. Another useful way to define a set is by specifying a property that the elements of the set have in common. The notation P(x) is used to denote a… …   Wikipedia

• predicate logic — noun a) The generic term for symbolic formal systems like first order logic, second order logic, many sorted logic or infinitary logic. b) First order logic. <! See . See Also: predicate calculus …   Wiktionary

• monadic predicate logic — noun The fragment of predicate logic in which all predicate letters are monadic (that is, they take only one argument), and there are no function letters …   Wiktionary

• Extension (predicate logic) — The extension of a predicatendasha truth valued functionndashis the set of tuples of values that, used as arguments, satisfy the predicate. Such a set of tuples is a relation.For example the statement d2 is the weekday following d1 can be seen as …   Wikipedia

• predicate calculus — Logic. See functional calculus. Also called predicate logic. [1945 50] * * * Part of modern symbolic logic which systematically exhibits the logical relations between propositions involving quantifiers such as all and some. The predicate calculus …   Universalium

• Logic programming — is, in its broadest sense, the use of mathematical logic for computer programming. In this view of logic programming, which can be traced at least as far back as John McCarthy s [1958] advice taker proposal, logic is used as a purely declarative… …   Wikipedia

• Logic and the philosophy of mathematics in the nineteenth century — John Stillwell INTRODUCTION In its history of over two thousand years, mathematics has seldom been disturbed by philosophical disputes. Ever since Plato, who is said to have put the slogan ‘Let no one who is not a geometer enter here’ over the… …   History of philosophy

• Logic (disambiguation) — Logic is the study of the principles and criteria of valid inference and demonstration.Logic may also refer to:In logic and mathematics*A branch of logic: **Inductive logic, also called induction or inductive reasoning **Informal logic, the study …   Wikipedia

• Logic in computer science — describes topics where logic is applied to computer science and artificial intelligence. These include:*Investigations into logic that are guided by applications in computer science. For example: Combinatory logic and Abstract interpretation;… …   Wikipedia

• Predicate — or predication may refer to:*Predicate (mathematics), a relation, or the boolean valued characteristic function or indicator function of a relation *Predicate (logic), a fundamental concept in first order logic **in Bertrand Russell s theory of… …   Wikipedia