Precisely, if a pointfree funcoid is defined on a lattice (or semilattice) with a least element , then because a lattice (semilattice) is a relational structure defined by a set of propositional formula, then we have the following operations and relations:
- meet and join operations on our lattice
- the least element of the lattice (a constant symbol)
- the standard identities of lattice considered as an algebraic structure (and also the obvious identities for the least element)
What are applications of the curious fact that every funcoid is a structure defined by propositional formulas? I don’t yet know.