2. Predicate logic

Definition (first-order predicate logic). First-order predicate logic or sentential logic or statement logic is a branch of logic that deals with quantified variables, so that rather than propositions such as "Socrates is a man" in propositional logic, there are formulas such as "There exists x such that x is Socrates and x is a man".

Historically, it was initially a formalization of mathematical language and reasoning, proposed by G. Frege between the end of the 19th and the beginning of the 20th century, and "popularized" by B. Russel and A. N. Whitehead (1910-1913). Predicate logic was introduced to the mathematical community...