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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 ∃ 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.

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

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