Title: Functional Conceptual Substratum as a New Cognitive Mechanism for Mathematical Creation,
Abstract: We describe a new cognitive ability, i.e., functional conceptual substratum,
used implicitly in the generation of several mathematical proofs and
definitions. Furthermore, we present an initial (first-order) formalization of
this mechanism together with its relation to classic notions like primitive
positive definability and Diophantiveness. Additionally, we analyze the
semantic variability of functional conceptual substratum when small syntactic
modifications are done. Finally, we describe mathematically natural inference
rules for definitions inspired by functional conceptual substratum and show
that they are sound and complete w.r.t. standard calculi.