This chapter explores the algebraization of annotated paraconsistent logics through the development of Pτ-algebras and their extension to monadic Curry algebras Qτ. Annotated logics are functional, two-sorted logics indexed over finite lattices, and are paraconsistent, paracomplete, and often non-alethic. The chapter formalizes the algebraic counterpart of these systems by introducing Pτ-algebras, where hyper-literals and complex formulas are treated within a classical implicative lattice extended with negation and annotation operations. Representation theorems show that Pτ-algebras are generalizations of Boolean algebras associated with clopen sets in Stone spaces. The framework is then extended to first-order systems with quantifiers via Qτ-monadic algebras, providing algebraic models for predicate annotated logics. Two distinct paths of Boolean and monadic algebra association—based on full and complex elements—are analyzed, and their representation theorems established. These structures offer deep insight into functional reasoning with incomplete and inconsistent information, opening avenues for further investigations in logic and knowledge representation.