Abstract: This paper has, as its point of departure, the foundational
axiomatic theory of E. De Giorgi (1996, Scuola Normale
Superiore di Pisa, Preprints di Matematica 26, 1), based on two
primitive notions of quality and relation. With the introduction of
a unary relation, we develop a system totally based on the sole
primitive notion of relation. Such a modification enables a definition
of the concept of dynamic unary relation. In this way we construct a
simple language capable to express other well known theories such
as Robinson-s arithmetic or a piece of a theory of concatenation. A
key role in this system plays an abstract relation designated by “( )",
which can be interpreted in different ways, but in this paper we will
focus on the case when we can perform computations and obtain
results.