Existential graph

An existential graph is a type of diagrammatic or visual notation for logical expressions, proposed by Charles Sanders Peirce, who wrote on graphical logic as early as 1882, and continued to develop the method until his death in 1914.

The graphs

Peirce proposed three systems of existential graphs:

alpha, isomorphic to sentential logic and the two-element Boolean algebra;

beta, isomorphic to first-order logic with identity, with all formulas closed;

gamma, (nearly) isomorphic to normal modal logic.

Alpha nests in beta and gamma. Beta does not nest in gamma, quantified modal logic being more than even Peirce could envisage.

Alpha

The syntax is:

The blank page;

Single letters or phrases written anywhere on the page;

Any graph may be enclosed by a simple closed curve called a cut or sep. A cut can be empty. Cuts can nest and concatenate at will, but must never intersect.

Any well-formed part of a graph is a subgraph.

The semantics are:

The blank page denotes Truth;

Letters, phrases, subgraphs, and entire graphs may be True or False;

This page contains text from Wikipedia, the Free Encyclopedia - https://wn.com/Existential_graph

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Existential graph

The graphs

Alpha

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