that looks like the Tiger, and the Dog that looks like the Wolf : Felids and Canids etc. Thus, a true hierarchy (taxonomy) of categories (or classes, in a broad meaning) can be constructed, starting from the most general (Animals) to the most particular (Species like Cat, Dog, Horse, etc.). This "systematic" is founded on a hierarchy of discriminant characters (nature of anterior limbs, of food, etc.) that are more or less accessible; for example, on what criteria can the distinction between Felids and Canids be based ?

The specialist is able to recognize things at a glance : he is an expert of his domain. But in order to understand, to know, he needs to analyze the reality more precisely. It is only after having done (or read) various descriptions of Felids, that himself (or another specialist before him) will be able to state the definition of the class named Family Felidaeand state that it can be distinguished from Canidae (among other things) by the fact that the posterior teeth bear cutting edges (they are named carnassials), while they are simple molars among Dogs.

We can notice that the "distinction between Canids and Felids" covers two dual approaches. In one hand, from a classificatory point of view, we learn by a generalization process that the character "presence of carnassials" synthetizes (or subsumes) all that has been observed on the different kinds of Felids concerning their posterior teeth. In the other hand, from an identification point of view, we deduce by analyzing the fact that Pussy bears carnassials, that it is a Felid and not a Canid. Whatever the approach, we had to deal with the description of posterior teeth; it is what we will call a local description.

2.1.1

Compositional logic

The description of an entity (let say a cat or a dog) is a composition of local descriptions that correspond to everithing that is observable and thus describable.

The description process is not ordered at random, but follows some logic which can be recognized. Whereas a cat or a dog both have a body, a head, four legs and a tail (they inherit all that because they belong to the Mammal class), it would be unconformist to begin the description by the tail; beginning it with the legs would be curious, unless the descriptor is an ant; but the choice between the body and the head is open. In fact, this logic is a matter of specialists who are the only ones to make an agreement on the definition of the most "natural" way for ordering the local descriptions. If it is the head that comes first, then the description will begin by its own characters, like its shape, size, color etc., by its connections with other parts, and then, following in turn a non arbitrary order, will continue with the description of its subparts (eyes, mouth, nose, ears etc.). And so on.

This decomposition into subparts is a basic mechanism; it is repeated as many times as necessary to reach the desirable level of detail (which, remember, depends on the intended use). Thus, we can agree upon an "exploratory tree", where at each node of we have a local description, and where each branch defines a relation between parts and subparts. This tree must provide all situations that may possibly be obesrved, including particular cases and exceptions, without introducing arbitrary limitations. From this point, the tree is generally thicker thannecessary for each particular description situation, and some branches can be proved to be irrelevant (without significance).

In particular, when describing, we use an automatic pruning mechanism that makes sense. Thus, when we know that one part is absent, all descriptions on its subparts become irrelevant; likewise, if for example I am describing the farm watch-dog, and it doesn't want to open its mouth, I would greatly prefer not to have to describe its teeth or its tongue. This illustrates a common situation encountered when describing natural objects, where some of the local descriptions are not possible because of the observational situation (part hidden or presently unobservable), or because the specimen to be described is not complete. We can postulate that when a local description is absent, it means that its corresponding part is unknown; conversely, when we state that this part is absent, this brings an information that must be stated explicitly in the description.