Nobody can say for certain who invented the truth table
The truth table is among the most familiar tools in logic, yet its origin is murky. Ludwig Wittgenstein and Emil Post usually get credit for the grid layout, perhaps independently, while a long list of others from Philo to Peirce anticipated the idea. One historian concluded that no single person deserves the title.
Propositional logic, also called sentential calculus or zeroth-order logic, studies statements that are either true or false and how they combine. Simple or atomic sentences are joined by connectives for not, and, or, if-then and if-and-only-if to form compound, or molecular, ones. Unlike first-order logic it has no quantifiers or predicates about objects, yet all its machinery sits inside first-order and higher-order logic, making it their foundation. In the classical version every formula takes exactly one of two truth values, and the law of excluded middle holds.
Only declarative sentences count. A question or a command has no truth value and belongs to specialised nonclassical systems. An argument pairs a set of premises with a conclusion said to follow from them, as in reasoning from the claim that rain implies cloud. The study is typically carried out in a formal language where letters stand for propositions and various symbols, including historical systems such as Polish notation, stand for the connectives.
The Stoic Chrysippus, in the 3rd century BC, is often credited with the first deductive system centred on propositions rather than on the terms of Aristotle's syllogisms. Most Stoic writings were lost, and their logic faded sometime between the 3rd and 6th centuries CE, only to be revived in the 20th century. Leibniz developed a symbolic calculus in the 17th and 18th centuries, but it was little known, so George Boole and Augustus De Morgan reinvented much of it on their own.
Gottlob Frege's predicate logic built on the propositional kind and opened a new era, but refinements kept coming. Gerhard Gentzen and Stanisław Jaśkowski devised natural deduction, and Evert Willem Beth introduced truth trees. For truth tables, ideas in Frege and Bertrand Russell mattered, and figures credited with tabular versions include Jan Łukasiewicz, John Venn and Clarence Irving Lewis.
Source: Propositional logic
