Graphical representations of intersection of sets as logical combinations are much older than Venn. Euler and Leibniz are often quoted and the current Wikipedia article also quotes Ramon Llull but I do not really find the illustrations provided in the Wiki Commons for Llull very compelling.
I expect that these kind of ideas can be found in many other places and even older times, perhaps in disguise.
In this context I find the heraldic uses of theological diagrams such as shown here quite fascinating as a kind of medieval fashion statement.
Do you know of older examples of graphical representation of logical and/or set relations, for instance of Chinese, Arabic and Greek origin ?
(ps: at least one of the tags is a joke)