Difference between revisions of "Predicate logic"

Latest revision as of 08:33, 20 April 2016

In mathematical logic, predicate logic is the generic term for symbolic formal systems.

Description

Predicate logics includes:

• First-order logic
• Second-order logic
• many-sorted logic
• Infinitary logic

This formal system is distinguished from other systems in that its well-formed formulae contain variables which can be quantified.

Two common quantifiers are the existential ∃ ("there exists") and universal ∀ ("for all") quantifiers.

The variables could be elements in the universe under discussion, or perhaps relations or functions over that universe. For instance, an existential quantifier over a function symbol would be interpreted as modifier "there is a function".

History

The foundations of predicate logic were developed independently by Gottlob Frege and Charles Sanders Peirce.

Informal usage

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.

Modal logic

Predicate logics also include logics mixing modal operators and quantifiers. See Modal logic.

See also

• Charles Sanders Peirce
• First-order logic
• Formal system
• Infinitary logic
• Logic
• Many-sorted logic
• Mathematical logic
• Modal logic
• Object-role modeling
• Second-order logic
• Symbol
• Well-formed formula

External links

• Predicate logic @ Wikipedia