# Formal Semiotic Zoo

The World-Famous UC San-Diego Semiotic Zoo  was designed to present a collection of semiotically challenged samples of the academic discourse (announced as "captured live in the academic jungles" :). My idea is to create here a special  branch for collecting funny samples of  (i) quasi-formal academic discourse, which only looks formal but turns out  senseless under a more careful consideration; and (ii) dual samples of  quasi-reasonable discourse about precise subjects, which only looks reasonable but turns out senseless  under an evident and straightforward formalization.  During my wandering in the notational jungles of computer science literature, I've encountered  amazing exhibits of both types of creatures, which could be interesting for the  general public.

A typical example of quasi-reasonable discourse (which I encountered more than once in computer science papers) is a half-page or so reasoning, which, after an evident and direct formalization, turns out to be a "proof" that the ordinary subset relation is transitive: If A Ì B and B Ì C, then A Ì C.  Its "dual twin" is a popular in conceptual modeling of  90s construct of may-be relationship between entities, postulated  to be transitive: statements A may-be B and B may-be C for concepts A,B,C  (for example, Student, Employee, Patient) imply A may-be C. However, a bit more careful analysis reveals  the following: normally, extensions of concepts are assumed to be disjoint by default, [[A]] Ç [[B]] = Æ, while the statement A may-be B means the possibility [[A]] Ç [[B]] ¹Æ (for some states of the system). Note, however, that [[A]] Ç [[B]] ¹Æ  and [[B]] Ç [[C]] ¹ Æ do not necessarily imply that [[A]] Ç [[C]] ¹ Æ.

There are more interesting exhibits  in my archive but their presentation needs more space. Consider, for example, the following one taken from a  big article published in ACM TODS in 1999:

What the authors actually want to say is almost what they wrote above but the target of the mapping A, or W in the example, is a two-element set P= {0,1} rather than vague "statement regarding A".  Indeed, in syntax we have predicate formulas like works-for(p,c,d), whose semantic meaning are predicate mappings like

[[works-for]]: T1 ´ T2 ´ D ® {0,1}

making formulas relations of the corresponding arity. Thus, in the example above, P is a set {0,1} and W is a set of triples (p,c,d) (constituting, probably, what the authors call statements) for which W(p,c,d) = 1.  In other words, W  is a ternary relation presented by its characteristic function. This simple construction is explained in any undergraduate textbook on logic. Contrary to that, the authors say that the target set of the mapping W, the set P,  is a set of statement, that is, a relation, thus coming to an absurd. This absurd is further cast into a bold statement:

Working in this way with formalities, the authors formulate a set of rules for a reasonable entity-relationship (ER) modeling. As an example of their rules applications, they consider the ER-diagrams presented below on the left and show that it  does not satisfy the Rules. Then they rebuild the diagram according to the Rules and come to the diagram on the right. In a lengthy consideration, the authors then state that the diagram on the right is a correct  ER-model of the universe while the left diagram is deficient.

Although the way the authors work with formalities prepares the reader for anything possible, the result of their comparative analysis of the ER-diagrams is still astonishing: for anyone who really worked with ER-diagram in practical applications, the left diagram gives a quite transparent model of the universe while the right one looks really weird. Nevertheless, the authors so much believe in their Rules that ready to sacrifice even the ordinary common sense.  All this could be just a funny curious sample unless it were the contents of a big article published in a peer-reviewed and elite ACM TODS journal.

A nice sample of quasi-reasonable discourse can be found in an article published in an ACM Communications in 2004. A detailed (and I believe instructive) analysis of the sample can be found here  (look here for the article itself). I submitted it to CACM but they declined publishing saying that it was too long and technical. To make it readable, I rearranged the text into a short one-page article, Why 3D is Better than 2D for Representing Spatial Figures, demonstrating the essence of the exhibit in a transparent way.  It was not accepted either :)

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