Short answers, pulled from the story.
Aristotle developed the first systematic study of logic known as term logic or syllogistics in the 4th century BCE. His work included the Organon and Prior Analytics which introduced the concept of the syllogism involving three propositions.
Gottlob Frege published his Begriffsschrift in 1879 to mark the birth of modern logic. This work introduced the notion of quantifier in graphical notation and revolutionized the field by articulating the internal structure of propositions.
Intuitionistic logic is a restricted version of classical logic that excludes rules like double negation elimination and the law of excluded middle. It establishes truth by verification using a proof rather than accepting that every proposition is either true or false.
Claude Shannon showed how Boolean logic can be used to understand and implement computer circuits using electronic logic gates. The truth values of propositions are represented by voltage levels to simulate logic functions.
Computability theory studies effective procedures to solve calculation problems and determines whether an algorithm can be found to decide if a claim is true. It uses theoretical tools such as Turing machines to explore these issues.