Two-valued states on Baer ${}^{\ast }$-semigroups

In this paper we develop an algebraic framework that allows us to extend families of two-valued states on orthomodular lattices to Baer ${}^{\ast }$-semigroups. We apply this general approach to study the full class of two-valued states and the subclass of Jauch-Piron two-valued states on Baer ${}^{\ast }$-semigroups.