The Second Venn Diagrammatic System
We present syntax and semantics of a diagrammatic language based on Venn diagrams in which a diagram is not read as a statement about sets, but as a set itself. We prove that our set of rules is sound and complete with respect to the intended semantics. Our system has two slight advantages in relation to the systems we usually encounter in the literature. First, the drawing of diagrams for terms is made inside the system, i.e., by a completely mechanical process based just on the rules of the system. Second, as a consequence, the validity of an inclusion is also verified inside the system and does not depend on any other means than those afforded by our set of rules. These characteristics are absent in the majority of the Venn diagrammatic systems.
Keywordsdiagrammatic systems Venn diagrams soundness completeness
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