The branch of formal logic, also called functional calculus, that deals with representing the logical connections between statements as well as the statements themselves.
See also
Gödel's First Incompleteness Theorem, Gödel's Second Incompleteness Theorem, Logic, Predicate, Propositional Calculus
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Weisstein, Eric W. "Predicate Calculus." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/PredicateCalculus.html