  The paper introduces the notion of state for involutive bisemilattices, a
variety which plays the role of algebraic counterpart of paraconsistent weak
Kleene logic and whose elements are represented as Plonka sum of Boolean
algebras. We investigate the relations between states over an involutive
bisemilattice and probability measures over the (Boolean) algebras in the
Plonka sum representation and, the direct limit of these algebras. Moreover, we
study completition of involutive bisemilattices, as pseudometric spaces, and
the topology induced by the pseudometric.
