Existential graph
[4] Thus, the development of an iconic, graphic and – as he intended – intuitive and easy-to-learn logical system was a project that Peirce worked on throughout his life.
Although considered by their creator to be a clearly superior and more intuitive system, as a mode of writing and as a calculus, they had no major influence on the history of logic.
[8] From 1963 onwards, works by Don D. Roberts and J. Jay Zeman, in which Peirce's graphic systems were systematically examined and presented, led to a better understanding; even so, they have today found practical use within only one modern application—the conceptual graphs introduced by John F. Sowa in 1976, which are used in computer science to represent knowledge.
However, existential graphs are increasingly reappearing as a subject of research in connection with a growing interest in graphical logic,[9] which is also expressed in attempts to replace the rules of inference given by Peirce with more intuitive ones.
The semantics are: Hence the alpha graphs are a minimalist notation for sentential logic, grounded in the expressive adequacy of And and Not.
The alpha graphs constitute a radical simplification of the two-element Boolean algebra and the truth functors.
If a graph can be reduced by steps to the blank page or an empty cut, it is what is now called a tautology (or the complement thereof, a contradiction).
If the "shallowest" part of a line of identity has even depth, the associated variable is tacitly existentially (universally) quantified.
Add to the syntax of alpha a second kind of simple closed curve, written using a dashed rather than a solid line.
Peirce proposed rules for this second style of cut, which can be read as the primitive unary operator of modal logic.
In a series of papers beginning in 1867, and culminating with his classic paper in the 1885 American Journal of Mathematics, Peirce developed much of the two-element Boolean algebra, propositional calculus, quantification and the predicate calculus, and some rudimentary set theory.
"[12] Otherwise they attracted little attention during his life and were invariably denigrated or ignored after his death, until the PhD theses by Roberts (1964) and Zeman (1964).
