diagrammatic-reasoning

Diagrammatic reasoning for Logic Graphs

Algorithm

• build a logic graph for the initial concept
• build a tree applying the rules until it is possible:

  • ⊓⁺-rule:

    

  • ⊓^--rule:

    

  • ∃⁺-rule:

    

  • ∃^--rule:

    

• if each branch of the tree contains a clash, the initial concept is inconsistent. Clash:

  

• otherwise, it is consistent

Examples

• inconsistent: a person who is vegan, but not a vegetarian, i.e. a person who eats only plants, but eats not only plants or dairy

Person ⊓ ∀eats.Plant ⊓ ¬(Person ⊓ ∀eats.(Plant ⊔ Dairy))

• consistent: a person who is vegan and vegeratian, i.e. a person who eats only plants and only plants or dairy

Person ⊓ ∀eats.Plant ⊓ ∀eats.(Plant ⊔ Dairy)

Comparison

• Logic Graphs

• Concept Diagrams

• Relation Graphs

We compare the complexity of visual syntaxes regarding their graph-theoretic terms.

	N of nodes	N of edges	Depth
LG	10	2	3
CD	11	2	3
RG	13	5	4