Predicate logic
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- For the specific term, see First-order 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 and universal 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 an axiomatized form of predicate logic, and the predicate logic to be derived from an informal, more intuitive development.[1]
[edit] Footnotes
- ^ Among these authors is Stolyar, p. 166. Hamilton considers both to be calculi but divides them into an informal calculus and a formal calculus.
[edit] 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
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