Draft:Logical diagram

A logical diagram is a diagram used to represent a logical proof, proposition or concept.

History


The development of diagrammatic logic began with the square of opposition diagram created by Boethius and Augustine based on the 4 categorical propositions "Some S are P", "Some S are not P", "No S is P" and "All S are P". No further advancements in diagrammatic logic were made until the invention of Euler diagrams in the 18th century. Euler diagrams were intended to serve as visual representations of the various Aristotelian moods. The next advance in diagrammatic logic came in the form of the Venn diagram in 1880.

Pierce's Role
The most significant advancement in graphical logic in the 19th century was made by American logician and philosopher Charles Sanders Peirce who in 1882 created a system of graphical logic referred to as existential graphs composed of three subsystems the alpha, beta and gamma graphs. Peirce was dissatisfied with the existing logical notation and wanted to create a system in which the signs resembled what they denoted.

Alpha graphs are isomorphic to Boolean algebra, beta graphs to first order logic with equality and gamma graphs are (partially) isomorphic to modal logic. Alpha graphs are both sound and complete.

Semantic Tableaux
Semantic tableaux is a type of tree diagram which is used as a proof procedure for propositional and predicate calculus, a proof consists of splitting the given formula into several sub-formulae which are each either proven or refuted.

Conceptual Graphs
Conceptual graphs are a graphical representation of first order logic formulae.

Euler and Venn diagrams


Euler and Venn diagrams are a notation for set membership and intersection. Venn diagrams were created to be a more expressive version of Euler diagrams for the purpose of teaching and would became widely used in probability, statistics, logic and set theory.

Advantages
Diagrammatic logic is seen as a more intuitive notation than symbolic logic and because of this is commonly used as a teaching tool. Proofs in existential graphs specifically are much shorter than symbolic proofs.

Disadvantages
Diagrammatic logic has been seen as being overly cumbersome, complex and not suited for practical use.