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

  • Stefano Aguzzoli
  • Matteo Bianchi
  • Brunella Gerla
  • Diego Valota
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, 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.

Keywords

Probability measures in non-classical logics Gödel propositional logic Gödel\(_\varDelta \) propositional logic Free algebras 

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Stefano Aguzzoli
    • 1
  • Matteo Bianchi
    • 2
  • Brunella Gerla
    • 2
  • Diego Valota
    • 1
  1. 1.Department of Computer ScienceUniversità degli Studi di MilanoMilanItaly
  2. 2.Dipartimento di Scienze Teoriche e ApplicateUniversità degli Studi dell’InsubriaVareseItaly

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