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Probability Measures in Gödel\(_\varDelta \) Logic

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Symbolic and Quantitative Approaches to Reasoning with Uncertainty (ECSQARU 2017)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 10369))

Abstract

In this paper we define and axiomatise finitely additive probability measures for events described by formulas in Gödel\(_\varDelta \) (G\(_\varDelta \)) propositional logic. In particular we show that our axioms fully characterise finitely additive probability measures over the free finitely generated algebras in the variety constituting the algebraic semantics of G\(_\varDelta \) as integrals of elements of those algebras (represented canonically as algebras of [0, 1]-valued functions), with respect to Borel probability measures.

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Author information

Authors and Affiliations

  1. Department of Computer Science, Università degli Studi di Milano, via Comelico 39/41, 20135, Milan, Italy

    Stefano Aguzzoli & Diego Valota

  2. Dipartimento di Scienze Teoriche e Applicate, Università degli Studi dell’Insubria, via Mazzini 5, 21100, Varese, Italy

    Matteo Bianchi & Brunella Gerla

Authors
  1. Stefano Aguzzoli
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  2. Matteo Bianchi
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  3. Brunella Gerla
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  4. Diego Valota
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Corresponding author

Correspondence to Stefano Aguzzoli .

Editor information

Editors and Affiliations

  1. IDSIA, Lugano, Switzerland

    Alessandro Antonucci

  2. ONERA, Toulouse, France

    Laurence Cholvy

  3. Aix-Marseille University, Marseille, France

    Odile Papini

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Aguzzoli, S., Bianchi, M., Gerla, B., Valota, D. (2017). Probability Measures in Gödel\(_\varDelta \) Logic. In: Antonucci, A., Cholvy, L., Papini, O. (eds) Symbolic and Quantitative Approaches to Reasoning with Uncertainty. ECSQARU 2017. Lecture Notes in Computer Science(), vol 10369. Springer, Cham. https://doi.org/10.1007/978-3-319-61581-3_32

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  • DOI: https://doi.org/10.1007/978-3-319-61581-3_32

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-61580-6

  • Online ISBN: 978-3-319-61581-3

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