Sentence Negation and Term Negation as Syntactic Operations in Diagram Logic

A formal treatment of negation operation in diagram logic is presented. Syntactic definitions of sentence negation and term negation are given in the \({\text {Venn}}_{\text {i}}\) diagram system. The difference between sentence negation and term negation is established in the language of diagrams. The syntactic way of negating a well-formed diagram does not increase the expressiveness power of the logical system. However, it can be very useful for quickly constructing diagrams that are in opposition relation to a given diagram.