This chapter develops the algebraic framework of Pn-algebras, a class of structures that formalize reasoning within paracomplete logical systems—logics that deny the Principle of Excluded Middle. Originating from the Pn calculi proposed by da Costa and Marconi, these algebras generalize classical structures such as Boolean and Heyting algebras to accommodate indeterminate propositions. The chapter explores the formal definition and properties of Pn-algebras, focusing on the P1-algebra and its role in modeling the deductive structure of paracomplete reasoning. Propositional Pn-algebras are introduced as generalizations of Rosenbloom’s propositional Boolean algebras, and their non-monotonic negation operators are analyzed. Key results include representation theorems, the formalization of deductive systems and filters, and the study of homomorphisms. The chapter concludes with soundness and completeness theorems for P1-calculus, establishing a robust correspondence between syntactic and algebraic semantics for paracomplete logic.