Probability Measures in the Logic of Nilpotent Minimum

Abstract

We axiomatize the notion of state over finitely generated free NM-algebras, the Lindenbaum algebras of pure Nilpotent Minimum logic. We show that states over the free n-generated NM-algebra \({{\fancyscript{NM}_{n}}}\) exactly correspond to integrals of elements of \({{\fancyscript{NM}_{n}}}\) with respect to Borel probability measures.