13 Facts About Predicate logic

Foundations of first-order Predicate logic were developed independently by Gottlob Frege and Charles Sanders Peirce.

Predicate logic takes an entity or entities in the domain of discourse and evaluates to true or false.

Unlike natural languages, such as English, the language of first-order Predicate logic is completely formal, so that it can be mechanically determined whether a given expression is well formed.

The terms and formulas of first-order Predicate logic are strings of symbols, where all the symbols together form the alphabet of the language.

Tarski and Givant showed that the fragment of first-order Predicate logic that has no atomic sentence lying in the scope of more than three quantifiers has the same expressive power as relation algebra.

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Unlike propositional logic, first-order logic is undecidable, provided that the language has at least one predicate of arity at least 2.

However, the compactness theorem can be used to show that connected graphs are not an elementary class in first-order logic, and there is no formula f of first-order logic, in the logic of graphs, that expresses the idea that there is a path from x to y Connectedness can be expressed in second-order logic but not with only existential set quantifiers, as enjoys compactness.

Instance, first-order Predicate logic is undecidable, meaning a sound, complete and terminating decision algorithm for provability is impossible.

Many-sorted first-order Predicate logic allows variables to have different sorts, which have different domains.

Many-sorted first-order Predicate logic is often used in the study of second-order arithmetic.

Fixpoint Predicate logic extends first-order Predicate logic by adding the closure under the least fixed points of positive operators.

Characteristic feature of first-order logic is that individuals can be quantified, but not predicates.

Second-order Predicate logic extends first-order Predicate logic by adding the latter type of quantification.