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 Mundiciʹs 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.