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
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 be an axiomatized form of predicate logic, and the predicate logic to be derived from an informal, more intuitive development.
- 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