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.
Probability measures in the logic of Nilpotent Minimum / S. Aguzzoli, B. Gerla. - In: STUDIA LOGICA. - ISSN 0039-3215. - 94:2(2010), pp. 151-176. [10.1007/s11225-010-9228-8]
Probability measures in the logic of Nilpotent Minimum
S. AguzzoliPrimo
;
2010
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.
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