Abstract
A very general structure in mathematics is a function system, that is a structure 𝒯 = ⟨U𝒯, Ω𝒯, Λ𝒯 ⟩, where U𝒯 is a finite universe set and Ω𝒯 is a finite set of functions ai: U →Λ𝒯. In this paper we use a function system to develop a mathematical theory of the indiscernibility. More in detail, we first use a natural equivalence relation induced by any function subset A ⊆Ω𝒯 to introduce a complete lattice of set partitions of U𝒯. We prove several properties of this order structure and we develop two specific cases of study concerning directed and undirected graphs. Next, for finite function systems we introduce two approximation measures that have a deep similarity with the Lebesgue measure and with the conditional probability. Also in this case we provide two specific cases of study on directed and undirected graphs.
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