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. Mathematical logic is a subfield of Logic and Mathematics with close connections to Computer science and Philosophical logic. In formal logic, a formal system (also called a logical system, a logistic system, or simply a logic Formal systems in mathematics consist First-order logic (FOL is a formal Deductive system used in mathematics philosophy linguistics and computer science In Logic and Mathematics second-order logic is an extension of First-order logic, which itself is an extension of Propositional logic. Many-sorted logic can reflect formally our intention not to handle the universe as a homogenous collection of objects but to partition them in a way that is similar to types Those unfamiliar with Mathematical logic or the concept of Ordinals are advised to consult those articles first This formal system is distinguished from other systems in that its formulas contain variables which can be quantified. In Mathematical logic, a formula is a type of Abstract object a token of which is a Symbol or string of symbols which may be A variable (ˈvɛərɪəbl is an Attribute of a physical or an abstract System which may change its Value while it is under Observation. Quantification has two distinct meanings In Mathematics and Empirical science, it refers to human acts known as Counting and Measuring Two common quantifiers are the existential ∃ and universal ∀ quantifiers. In Predicate logic, an existential quantification is the predication of a property or relation to at least one member of the domain In Predicate logic, universal quantification is an attempt to formalize the notion that something (a Logical predicate) is true for everything, or every The variables could be elements in the universe, or perhaps relations or functions over the universe. The domain of discourse, sometimes called the universe of discourse, logical discourse, or simply discourse, is an analytic tool used in Deductive 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. First-order logic (FOL is a formal Deductive system used in mathematics philosophy linguistics and computer science 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. ^[1]

Footnotes

1. ^ Among these authors is Stolyar, p. 166. Hamilton considers both to be calculi but divides them into an informal calculus and a formal calculus.

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