So what is all this fuss about the relation between inquiry and signs, as analyzed in Peirce’s theories of their structure and function and synthesized in his theory of information?

In many applications a “predicate” is a function from a universe of discourse X to a binary value in B = {0, 1}, that is, a characteristic function or indicator function f : X → B, and f⁻¹(1), the “fiber” of 1 under f, is the set of elements denoted or indicated by the predicate.