Dual Tableaux for First-Order Post Logics

Abstract

Emil Post’s doctoral dissertation [Pos21] included a description of an n-valued, functionally complete algebra, for a finite n ≥ 2. The notion of Post algebra was introduced in [Ros42]. The first algebraic formulation of Post algebras with a family of unary disjoint operations was presented in [Eps60]. In [Rou69] and [Rou70] an equivalent formulation of the class of Post algebras was given where monotone operations instead of disjoint operations were used. It became a starting point of extensive research and since then various generalizations of Post algebras have been developed, see e.g., [Ras73, Ras85, ER90, ER91]. Post algebras were also applied to a multiple-valued formalization of some logics of programs, see [Ras94].