How did Charles Sanders Peirce contribute to modern logic?

Charles Sanders Peirce was a foundational figure in modern logic, significantly advancing the field through his work on the algebra of logic and the logic of relations. His contributions include:12

• Logic of Relations: Peirce moved beyond the equational style of George Boole, developing techniques to handle relations within an algebraic framework. He emphasized the importance of transitive and asymmetric relations, which he used to express class inclusion and propositional connectives.12
• Quantification Theory: He introduced notation that resembled modern quantifiers, which were later adopted by Ernst Schröder and Giuseppe Peano, becoming the basis for widely used modern notation.12
• Tautology: Peirce was the first to develop the notion of tautology within the propositional calculus, providing a mechanical method for identifying statements that are true under all possible truth-value assignments.3
• Logical Systems: He created systems of logical graphs, including entitative and existential graphs, and explored three-valued logic, which admits a truth value between true and false.4

Peirce’s work was deeply influenced by his broader philosophical views, including his theory of semiotics, which viewed reasoning as a diagrammatic process.14