Peirce developed three varieties of Existential Graphs: Alpha, Beta, and Gamma. Alpha is the counterpart of truth-functional, or propositional logic, Beta is the counterpart of predicate, or quantificational, or first-order logic, and Gamma is the counterpart of modal logic. Below are some presentations laying out the details for the systems of Alpha and Beta. For Alpha, the important metalogical results of soundness and completeness are proven, and some thoughts are provided regarding automated Theorem Proving and Automated Proof Generation.
Alpha
Beta
Existential
Graphs