States on commutative basic algebras

The paper deals with states on commutative basic algebras that are a non-associative generalization of MV-algebras or, in other words, the algebraic semantics for a fuzzy logic which generalizes the Łukasiewicz logic in that the conjunction is not associative. States are defined in the same way as Mundici's states on MV-algebras as normalized finitely additive [0,1]-valued functions, and some results analogous to the results that are known from MV-algebras are proved.

► Commutative basic algebras are a non-associative generalization of MV-algebras. ► States are defined as Mundici's states on MV-algebras. ► The state space, if nonempty, is homeomorphic to the state space of some MV-algebra. ► States correspond to Borel probability measures on the space of state-morphisms.