What Is an AEG?

What are these things?

Alpha Existential Graphs (AEGs) are isomorphic to statements in propositional calculus. They are diagrammatic, and while Charles Peirce's design involves fewer symbols, fewer primitive connectives and fewer steps necessary for proofs as a consequence of involving more inference rules, the AEG system is able to reach all the same conclusions as propositional calculus.

What does this mean?

Propositional calculus, also called propositional logic, is a branch of mathematics concerning how to transform statements in order to determine their truth or falsity.

Primitive connectives, also called logical connectives or logical operators, connect statement letters together in propositional calculus. Examples include but are not limited to negation, conjunction, sometimes called logical AND, and disjunction, sometimes called logical OR.

Proofs are mathematical objects composed of a sequence of steps applied to reach a conclusion. As we can see, the notation for propositional logic proofs can appear complex, difficult to follow, and a bit overwhelming to parse through.

Fewer Symbols and Primitive Connectives?

Since any statement's truth or falsity in propositional logic can be determined through conjunction and negation, those are all the connectives we need! We don't even need a symbol for the former!

The Atom

These are the statement letters in this system and can take either True or False as truth values. They may be any one upper or lower case letter of the English alphabet. You may affectionately refer to them as "little guys."

The Cut

These are the negation connectives in this system, and they take the form of ellipses. Any atom or cut contained within a cut is considered to be negated. Note that cuts may be contained within other cuts. You may, then, describe an atom's or cut's depth in an AEG as a zero-indexed "cut level."

The Sheet of Assertion

Since Peirce developed this system when a computer was an occupation, a piece of paper, chalkboard, or otherwise large, writable space was intended to be the universe. We use the HTML canvas. Atoms and cuts placed on The Sheet, in the same cut level, are considered to be in conjunction with each other.

Atoms and cuts placed on The Sheet are considered to be in cut level zero.

Connecting All the Dots...

That's all there is to connect! With only these components, you may construct an equivalent graph form of any propositional logic statement in the AEG system. But, to manipulate these graphs, you also must learn about the inference rules for AEGs...