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Probability Measures in the Logic of Nilpotent Minimum

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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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Authors and Affiliations

  1. Dipartimento di Scienze dell’Informazione, Università degli Studi di Milano, via Comelico 39-41, Milano, Italy

    Stefano Aguzzoli

  2. Dipartimento di Informatica e Comunicazione, Università degli Studi dell’Insubria, via Mazzini 5, Varese, Italy

    Brunella Gerla

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  1. Stefano Aguzzoli
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  2. Brunella Gerla
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Correspondence to Stefano Aguzzoli.

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Aguzzoli, S., Gerla, B. Probability Measures in the Logic of Nilpotent Minimum. Stud Logica 94, 151–176 (2010). https://doi.org/10.1007/s11225-010-9228-8

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  • DOI: https://doi.org/10.1007/s11225-010-9228-8

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