As a result of theorem 4 we introduced the following definition of (ir)relevance: when the value of a point need not be known to assign a value to another point, we will say that (the value of) the first point is irrelevant for (the value of) the second point. Irrelevance is a "difference that makes no difference." Relevance is "a difference that makes a difference."

The notion “relevance” versus “irrelevance” always and only results from the assignment of a value, thus the result of the collapse of a lattice, so that a sublattice is not freely selected any more, because it already has been given a chosen value. Assigning a value to something is always twofold: the embedding is also given a value. In deciding "something" relevant one opts for "something" but simultaneously, hence with the same decision, something else happens (something that one can not choose). That is exactly the same relevance. The result of this decision is that, seen from the original freedom of choice between distinctions and without having to reformulate, there is a reduction of choice. The reality that is modeled in the original lattice is thus reduced to a part of that reality. For every action a decision is taken with the consequence that a number of options are made impossible. Successive decisions within the same distinction universe can only reduce the number of potentialities.

The modulo3 representation allows to encode a collapse uniquely. For example, the choice to give a the value <> (and thus give <a> the value of <<>>) is encoded in a two distinctions universe as (x-x-). The resulting relevant lattice has only four points : (x+x+), (x-x+), (x+x-), (x-x-).

We notice now that there is no difference between a point with representation (xxxxxx+--) and one with representation (x+--), except the universe in which they are represented. The irrelevant bits are marked with an x and the relevant bits with either + or -. The relationship thus introduced is referred to as the relation of (ir)relevance, and can now be examined in general.

We distinguish two values: "." and "x". The typographic point represents the value of a signature which is unknown, "x" represents a don't care. These are the only values available for a modulo3 bit position: either the bit position is a don't care, either the bit position has a signature (either - or +, in binary format this is 0 or 1).

The new values "." and "x" are each orthogonal involution : the orthogonal involution of "." is "x", the orthogonal involution of "x" is ".". An orthogonal involution we will also call an orthogonalisation. For example, the orthogonalisation of (xx.. xxx.) Is (..xx...x).

The relationship of (ir)relevance has two fundamentally different directions wich we indicate with the operations + versus ×. Note that + represents an operation and not a value. Note that × represents an operation and not a value. Since the values that are used with the relationship of (ir)relevance are "." and “x”, no confusion can occur.

The relationship is defined in the following table.

Note that we indicate the two directions for one relationship. If there is at least one bit relevant, than a+b is relevant, if there is at least one bit irrelevant then a×b is irrelevant and: a+b is not relevant only if both bits are irrelevant, a×b is relevant only if both bits are relevant.

The table is the easiest to memorize if one follows the classical sum and product rules for "x" as number-zero and "." as an arbitrary and unspecified positive number (this example by taking for each bit its square).

We may now construct the following table, which is fully analogous to the table of the 16 possible binary values of two distinctions. The brackets are now replaced by square brackets, by which we encode orthogonality ([] is the orthogonalisation of [[]], for example: a is orthogonal to [a]), the juxtaposition is replaced by ×, the combination of × and [ ] generates +. In the table we give in the first and last column the translation of the bit strings in function of both × and +.

The duality of the distinctions in this table is coded as with ordinary brackets, eg [a]×b is the dual of [a+[b]]. This allows to construct forms in which the two operations, × and +, occur. We will, however, avoid this and preferably only work with ×.

This table can be studied as follows: what is relevant in a×b, is also relevant in a. What is relevant in a, is also relevant in [[a]×[b]]. Conversely, what in [[a]×[b]] is irrelevant, is also irrelevant in a, is also irrelevant in a×b. Hence the relationship of relevance is a partial order relation with p+q (or [[p]×[q]]) and p×q (or [[p]+ [q]]) as extrema of the relationship.

By analogy with what we introduced in the relation of simultaneity, we can now introduce a symbol for the relationship of relevance. We use ≤ versus ≥ with the index r for relevance. The choice of the "greater than or equal to" symbol, and the "less than or equal to" symbol is justified because the relationship of relevance is a partial order relation. Indeed, we can also see the different orderings in a lattice either monotonous less relevant or monotonous more relevant. Every monotone path of points that would be followed has only one point at any level of the lattice (we choose to take the supremum of p and q as p+q, the infimum as p×q):

The pattern of the lattice is now well known, and will now show the relation of relevance between collapsed points, wherein the supremum of the whole lattice is an arbitrary potential point, and the infimum the all-zero vector.

Each of the points coded in the lattice has a complex relationship with different points of a potential lattice. It is not, because we are using the symbols a and b, that a and b are distinctions, a and b are, after all collapsed lattices, each coding for more than one collapsed points, which, however, share the same collapse.

For example: take as the coding for a (.x.x). This is a pattern of the following four possible collapsed points: (+x+x), (+x-x), (-x+x), (-x-x). That also means, as we take for b the coding (..xx) that a × b stands for the two collapsed points (+xxx) and (-xxx).

We say p is more relevant than q, with symbol p≥ _rq, when [p]×q can not be distinguished from the all-zero vector.

We say p is less relevant than q, with symbol p≤ _rq, when p×[q] can not be distinguished from the all-zero vector.